This question deals explicitly in how the mechanics of Pathfinder functions and not in how I should resolve this at the table; in Pathfinder, if a character is immune to an effect and then targeted by an ability that both permits a save and afflicts that effect, do they still roll a saving throw? For example, if a character immune to Paralysis is targeted by Hold Person, or if a red dragon is targeted by a fireball, are saving throws still 'supposed' to be rolled?
[RPG] Do you still roll a saving throw against effects that your character is immune to
pathfinder-1esaving-throw
Related Solutions
Scaling is possible.
I agree with @DavidCoffron for the most part on balance. This is a rather over-powered ability to have at lower levels and might be insigificant at higher levels.
The downsides from your link would likely translate to disadvantage (at least doing things that required that hand or both hands) rather than a -2 but that would be in your DM's wheelhouse as well. Those penalties are also non-combat related for the most part so they don't necessarily offer much in the way of offset in my opinion. But keeping these as penalties likely won't hurt anything, as there are Rings and Cloaks of Protection as well as partial cover and so on. Just be aware that you are breaking away from the core tenets of the 5E system by doing it.
I didn't stick with PF long enough to get into the idea of these Necrograft things.
However, if scaling is a must it is important to note that Saving Throws are calculated the same way for NPCs/Monsters as they are for PCs. Might not be stated explicitly but it is implicit in the design.
So to deconstruct the Save we proceed as follows:
Template is 8 + Proficiency Bonus + Ability Modifier
Base 8 + 2 (CR 1 Creature) + 0 (Likely Constitution as it is doesn't fit for Wisdom on this ability which is the ghoul's only other +0).
You could therefore work with your DM to apply your proficiency bonus and your Constitution modifier. This might, however, go against the premise on the Necrografts though.
To potential down-votes I know there is nothing explicit that says this is how it work, that I remember, but it is intuitive to work this way.
RAW, no.
Or, answering the body question instead, the spell ignores these features.
Spells do (only) what they say. The spell does not force a saving throw. For the monster's feature to be a "Specific beats general" case, it should explicitly state something along the lines of:
If this creature is affected by the sleep spell, it gets a X saving throw. The consequences for failing are Y. The consequences for succeeding are Z.
Neither of them do, and, as far as I'm aware, no creature or class has a feature worded like that, i.e., no feature states that "they get a saving throw" in any way. They simply have advantage against saving throws that already exist, which sleep doesn't provide.
A similar case is
The mirror image spell has no effect on magic missile, which doesn't involve an attack.
So, we could answer with the same logic:
The bugbear chief's feature Heart of Hruggek has no effect on sleep, which doesn't involve a saving throw.
Additional conjecture for my answer is that you would have to adjudicate what type of saving throw? Is it Wis? Con? What happens if the creature succeeds the saving throw? Is it simply not affected? Does the HP from sleep's HP pool that would have been used for that monster get reduced anyway? While these answers might be easy to adjudicate, none of them is answered by neither the spell description or the feature. Spells are (supposed to be) clear (that's the whole point of "Spells do what they say"), so, if you have to adjudicate so many things, this is probably not how the effect should be resolved.
As for "Why does the Bugbear Chief have a feature like that then?", I've created this question. NautArch has already provided examples. One of them, the symbol spell, has a possible effect that states:
Sleep. Each target must make a Wisdom saving throw and falls unconscious for 10 minutes on a failed save. A creature awakens if it takes damage or if someone uses an action to shake or slap it awake.
Best Answer
No Order of Operations Exists...
These are rules you'll have write. It's unfortunate in d20 that there's no quantified step-by-step order for combat and applying effects a la most trading card games. Were there, we could just say, "Immunity applies during step X, Damage Resolution, after Saving Throws but before Inflicting Effects," or whatever.
...But If You Want My Opinion
Yes, if only so the creature can choose to give up that saving throw.
Immunity shouldn't remove options everyone already has that aren't part of being immune. As everyone has the option of giving up a saving throw before knowing an effect's effect, immunity shouldn't change that.
Therefore when a creature is subject to an effect that requires a saving throw, the creature can choose to either make the saving throw or voluntarily give up (i.e. fail) that saving throw. Then the DM determines if the creature's immune to the effect.
Thus, unless the creature already knows an effect won't affect it (via a successful Spellcraft check, a successful Knowledge check that's revealed the opposition's abilities, or prior experience), the creature attempts the saving throw despite realizing an instant later that it possesses immunity to the effect.
That's because Pathfinder (and its antecedents) is a dangerous place, and what individuals can do varies wildly. A creature is safer if it always attempts saving throws versus affects, even if it thinks it might be immune to such effects because there's usually a random component to identifying effects, and being dumb gets it killed. Even a red dragon--who's immune to fire--will still make a saving throw versus the spell fireball [evoc] (Pathfinder Role-playing Game Core Rules 283) because there's no way to anticipate how a particular caster's fireball is going to differ from any other caster's fireball.
If immunity is checked first there's no opportunity to voluntarily give up the saving throw, and that opportunity should exist even if the creature's immune if for no other reason than to let the DM, when describing the spell's effect, tell the players that the creature appears to give up its saving throw, acting all awesome because the creature suspects he's immune.
If a Precedent's Absolutely Necessary
When spells are printed, they're printed with a Saving Throw first and the Spell Resistance after, so absent another order, those are checked in that order. Linking spell resistance to spell immunity is easy, but making the jump from spell immunity to immunity is harder, but, hey, the words are there.