First off, don't forget that there's a Sleep spell in the main book that uses Thaumaturgy (YS 293), which would make a good baseline.
Apart from that, it looks about right. I'm not sure you'd want to have the Aspect be "Terribly Sleepy", since invoking that wouldn't actually put them to sleep. Invoking an Aspect that implies something will happen when invoked (such as say, "Off Balance") doesn't make that happen; it just makes it easier for someone to make it happen. Invoking "Off-Balance" won't automatically knock someone over, you'd still have to roll Fists or Athletics or whatever to actually knock them over; invoking the Aspect would get you the +2/reroll making it much more likely.
It might be better to have the Aspect be "Light Sleeper" or "Catnapping", since that puts them out straight out (which is what you you want), but still lets people invoke to get a bonus to sneaking or whatnot, but at the same time implies that the target can be woken up easily.
From the writer, Fred Hicks:
biomancy is a tricky, poorly documented part of magic in the source
material. But, yes, it’d incorporate transformation magic, and its
healing elements likely manifest as accelerated medical care, only
occasionally branching into true “regeneration” type stuff at the
extremes.
With that in mind, I think that a Biomancer is more akin to a doctor than a cleric, which seems to fit the source material. Keep in mind, that this is an urban fantasy, so having an easy way to heal an extreme consequence (an arm being taken off, for instance) brings to mind the question of why is cancer still a problem, and (without going into too much detail) why are extreme wounds to characters in the source material such a problem.
That said, I'd look towards the character concept and the focus of the player in creating the character to how you might tailor things to make the concept work in your game, and make things satisfying to the player in combat.
In the Dresden Files combat, there are four basic conflict actions: Attack, Maneuver, Block, and Sprint. (ref YS199). Taking sprint out of the equation and reducing the actions to their simplest intent, these actions are meant to either protect the character (thus prolonging the conflict), damage the opposition (thus contributing towards the end of the conflict), or set up opportunities for one or the other.
An application of Biomancy that would fit within these rules is a Block. If someone is in combat, the Biomancer could focus himself on increasing their natural resistance to damage and their natural recovery. The description of the effect would reinforce the use of Biomancy i.e. instead of a kinetic shield stopping the bullet or altering it's path, the bullet impacts the target, but the biomantic energies were able to knit the damaged body before the effects of the shock could even register.
If this is not enough to satisfy the concept and you want to extrapolate the rules and/or use the FATE SRD rules, you can move beyond this. An example of mitigation of consequences is already given- and I think given the statement above about what the intent of what biomancy would be fits their example. So I'd concentrate on stress.
Looking at YS201, we see a definition for stress:
Stress is an abstract representation of the difficulties that threaten
to take someone out of a conflict. In a physical fight, stress can be
minor cuts, bruises, fatigue, and the like. In a social or mental
conflict, it might be loss of willpower, composure, or emotional
control...
As attacks inflict stress (which result in consequences), and blocks inhibit stress by increasing defense (resulting in less consequences), the only actual result of removing stress is to extend the conflict. This is the balancing effect to keep in mind. If one side has the ability to remove stress, and extend their staying power in the conflict, and the other one doesn't, you tip the balance in the favor of the side that can remove stress, though the fact that this is a transference in the case of non-rotes does mitigate this concern some.
With that caveat in mind, the first place one could look for an example of what could be done with removing in-combat stress is the FATE SRD. In the FATE SRD (based on Spirit of the Century), there is a skill, Science, which has a stunt Medical Attention [Science].
When using Science as first aid in the middle of a fight, the
character must take a full action with a target who’s not trying to do
anything else active (i.e., forfeiting his next action). Make a roll
against a target of Mediocre; if it succeeds with at least one shift,
the subject may remove a checkmark in his one-stress box on his
physical stress track. Every two shifts beyond the first improves this
effect by one; for example, with five shifts, a character can remove a
checkmark in his target’s three-stress box. Success can also be used
to “stabilize” someone who has taken a severe or lesser consequence
that would appear to be life-threatening (e.g., a Bleeding to Death
aspect) – in game terms, this has the effect of limiting the extent to
which the aspect can be compelled. A given person can’t be the target
of more than one first aid action in an exchange.
Under this approach, one would use an Evocation with the spell's intensity against the target of Mediocre and follow the same guidelines.
Another approach one could use is to look at stress as taken as an intensity of the blow, especially since each dot of stress is an increasing value, and the lower levels of stress won't help with higher intensity wounds. So if your Biomancer wanted to give someone the ability to clear their 4 stress box, they would require an effect with a 4 intensity. Knowing that, you can craft an evocation spell against that intensity.
Note that for balance's sake, and because this isn't explicitly laid out in the rules, the intensity might have to be altered, especially given that a moderate consequence removes 4 stress from the hit, and a mild removes 2, so the equivalency might be a bit different. But I think that these general guidelines would fit the spirit of the rules.
Best Answer
To get a grip on how much time Thaumaturgy takes, you'll want to skip to YS p. 268, "Adjudicating Preparation". Also note that if their Lore is sufficient, you can consider the wizard already prepared and it takes no more play time than an Evocation.
The significant unit of time for Thaumatury isn't a minute, or second, or even hour. Thaumaturgy isn't measured in game-world time units, but rather in game-play time units. Hence, the significant unit of time is the scene, and the amount of time it takes is a matter of GM pacing.
In essence, roleplay the preparation. Do they know what the ritual they need to do is? Their character has to actually do those things. Do they not know the ritual they need? Then they have to go find out and gather the knowledge and resources. Play that out as a quick montage, possibly with skill checks.
That's what the options for the player are there for: Invoke Aspects, Make Declarations, Accept or Inflict Consequences, and (for extreme cases) Skip Scenes.
None of those things should be done as a simple roll and move on. Play it. Playing it out is where the time comes from. Do they have a bloody handkerchief of the person they're trying to locate? That's great, but they still have to do all the FATE stuff to make it mechanically relevant, and to make it mechanically relevant they have to make it roleplaying-ly relevant by playing how it matters and how they use it. This is the beating heart of FATE, where the mechanics demand that roleplaying happen before you can use them. Ignoring this makes FATE fall flat. FATE is a game about showing why the mechanics are justified by playing them first, not by just telling the GM what mechanics are being used and skipping straight to their mechanical effect.
For some examples of what this looks like:
Make a declaration to create an Aspect about it. What are they doing with the handkerchief? Are they focusing their will on it, attuning themselves to the substance of the person they're trying to find? Are they using it to create the circle? Are they arranging it "just so" with a few other personal articles to create a "presence" of the person? Are they smearing symbols on a knife they're going to transform into a "compass"? Ask them what they're doing! What they do will determine what they roll to create the Aspect and what the Aspect will be. Don't just give it to them – make them earn it. Without doing that, you'll skip what makes magic in FATE actually fun to use.
Invoke Aspects. Same idea: they have to earn it by playing it. Players can't just say, "I'm invoking Dear to My Heart because I care about her a lot", they have to show it. They're going to have to roleplay some heart-rending stuff if they want that Aspect. It doesn't have to be long – in fact it can be very brief, as brief as a sentence. But it has to be there, or they don't get the Aspect. Put the fiction in place first, and the mechanics that belong will always be obvious.
Accept or Inflict consequences. In Storm Front, Harry didn't just say, "So I'm going to channel the storm now," and then he cast a spell at the demon. No, he agonised over exactly how dangerous that was, and then did it anyway. He didn't just vaguely channel the storm, he got hit by freaking lightning. He scorched and burned and ached. That is what your players need to do when they're accepting a consequence. The example in the book of the nasty ways consequences can be inflicted takes time too: torturing someone, or sacrificing a living victim, aren't instantaneous. The dark wizard is going to have to get a hold of them, bind them, and actually do the deed. You as the GM need to make that a scene, perhaps a pivotal one. That is where the casting time comes from.
Skip Scenes. This is the fall-back. It's actually the least interesting option, because it takes the player out of the scenes the others are part of. They still need to describe what's going on, else they don't get this option. It should never be: "Okay, I skip a scene to get more shifts." Even the book makes this clear: The player has to describe, even if only briefly, what they're doing that makes them have to skip a scene. Research in the library, ransacking their lab for that one component that they need, and so on.
It should be clear now where the time that Thaumaturgy takes comes from. It comes from all the stuff that the wizard has to do to actually pull off a complex spell, all that stuff that needs to be said by the player and done by the PC. It can sometimes be done as a montage: You don't have to describe every step to the library, just a sentence that evokes images of riffling through shelves, poring over books, and burning candles late into the night – stuff that shows time is passing, and why it's passing.
This is also why Thaumaturgy isn't always strictly better than Evocation: if the character has to actually do this stuff, the world isn't always going to wait for them. If they have to 1) declare an aspect, 2) invoke that and a few other aspects, 3) draw the ritual circle, 4) do the actual ritual, then at some point in that multiple-action process the Bad Guys are almost certainly going to have opportunities to cause problems. It might not even be direct interference – action that the player doesn't like might continue elsewhere.
If a PC wizard is casting Thaumaturgy in the middle of period where time is of the essence – an action scene, or when time is running out some other way – take this golden opportunity to make their life very, very interesting while they're distracted. Interact with their preparations and ritual. They run into exactly the person they want to avoid while trying to get to the library. They need to draw a circle but they only have chalk and it's raining – now what do they do instead? Do they shrug and forego the shift they could get, or do they scramble for an alternative way to create the circle?
Make it fun, make it interesting, play it out, and the time that Thaumaturgy takes will happen all by itself without counting it out.