Lucky you
Your panels are set up very advantageously to put in a generator transfer switch. All the loads you want to switch (but one) are already in a subpanel. This makes this super easy. It's almost like somebody planned it... Except the guy who put the pump circuit in the main panel did not get the memo.
You need to put a different transfer switch in between the two boxes. There are a couple ways to do this.
One is fit the subpanel with a manual interlock switch. This is a listed (offically tested) modification to the subpanel where it puts two breakers opposite from each other with a sliding plate so they can't both be on. Simple and cheap, and you may even be able to retrofit your existing panel. Must be thrown manually.
The other way is to pick a spot along the cable between the panels (or elsewhere if you don't mind rerouting cable), cut the cable, and insert the transfer switch inline. This will work with any kind of transfer switch, including automatic. You'll need to cut the cable on one side with enough slack to work, and the other side will be too short so you will have to replace that "half" of the run. So choose location and cut point very carefully to your advantage.
That one breaker in the wrong panel
The stuff you are imagining, you cannot do anything like that. In that approach, the options are break the law, backfeed the grid and kill linemen; or spend a king's ransom on more heavy cables than the underside of an NYC subway car, in a veritable Gordian knot of transfer switch wiring that nobody will be able to figure out after the fact. And the power company and inspector will absolutely hate it.
The right way is easy, if annoying: move the circuit to the subpanel. Extend the pump circuit, all wires, to the subpanel and land it on a double breaker, ground bar, and neutral if used. Do not continue to use the ground in the main panel, in fact if you make this splice inside the main panel, tape the ground wire with green tape to insulate it from the main panel. It's not the end of the world if it grounds accidentally, but grounds must go to the same panel the hots do.
I know that's a pain, but it's way less of a pain than anything else you could do legally.
Not room in the subpanel?
This happens a lot, some guy drove back from the subpanel store slapping himself on the back for saving $30... by buying barely enough spaces. Don't be that guy. You're going to need 6 right off the bat - 4 for the transfer switch and 2 for the well pump.
Worst case you may need to replace the subpanel, and fortujately that is DIY-possible because you can entirely shut off the panel at the main breaker. Also a great time to be looking for transfer switch friendly panels if you want to go that way. Don't scrimp - slap yourself on the back for buying twice as many spaces as you need today. The bigger panels often come with "bonus breakers" which save you some money too.
First, check out my answer to "What is a double-stuff breaker?"
Second, take a quick moment to educate yourself on "rule of six" panels. I am fairly sure you don't have one.
single pole vs tandem locations
Generally, common 1-pole breakers can go anywhere in the panel (except in Rule of Six panels in the top section, because that would put you over six).
Double-stuff breakers can only go in spaces designed for double-stuffs. A typical panel will allow this in 0, some or all of its spaces -- though "all" is becoming rare. The labeling on the panel will say where they are allowed. Newer panels also have "keying" which makes the wrong breaker impossible, though older ones do not, and there's always the wiseguy with a file defeating the keying.
do you use single until you upgrade to tandem?
Tandem is a downgrade. The breaker will perform more poorly and high loading on one side will make the other side more susceptible to nuisance trip. Much worse, double-stuffs are not available at all in AFCI or GFCI, and virtually every residential circuit today requires those. What's more, remodeling must be to new codes and that requires more circuits.
Double-stuffs are the mark of a cheap builder who decided to save $30 by buying a 20-space panel instead of the 42-space the house actually needs.
what does "circuit breaker was oversized" mean?
The breaker's job is to protect wires and devices. 14AWG wire needs 15A protection or it will overheat. Common receptacles need 20A protection or they will overheat. Certain devices need protection of a size they will specify.
An oversized breaker means somebody made a mistake, or swapped in a too-large breaker because he was overloading the circuit and got sick of the breaker tripping. Replace the correct breaker. Breakers are $5.
what's a normal breaker really called?
It's more defined by the absence of a label like duplex or quadplex. To be more specific, call it a 1-pole breaker or 2-pole breaker.
general rules?
Yah. Only use breakers listed for that panel. I certainly hope your panel is a Siemens/ITE because almost all your breakers are listed for those panels.
The Square D Homeline breaker in position 17 is the snake in the stick pile.
Now a lot of people go "oh, but they fit". Those people aren't qualified to decide whether they fit, that's UL's job. There are several brands of 1" breaker that will mutually snap in, but if you have any experience you'll notice the insertion force is all wrong. That's because the busbar blades are each shaped differently, and each breaker is made to mate with its family's busbar and not the others.
There is such a thing as a "classified breaker" made by one brand specifically for another brand's panel, but if square D made such a thing for Siemens, they would never market it as Homeline (HOM).
Best Answer
You have the wrong breaker for what you want to do here
The Eaton DNPL (aka BRD) type of breaker is a tandem or double-stuff breaker, that has two circuit breaker mechanisms inside it that share a line terminal, but have separate load lugs. These are used extensively to "cram" circuits into a panel, as we see in your panel.
However, since both of the breakers in a double-stuff are connected to the same leg or phase of the service, you cannot use one to feed a multi-wire branch circuit (like the one you propose) without overloading the neutral, since the hot wires in a MWBC must be on different legs or phases to allow only the difference in loads to flow down the neutral, rather than the sum of the loads.
If this were a regular branch circuit, you would need to replace the bottom rightmost DNPL1515 and the empty slot with a DNPL152015, then land the wires from the old DNPL1515 on the two outer poles and the new 12AWG wires on the two inner poles. However, this creates other problems, so read on for details.
You don't have the space for a GFCI breaker
The bigger problem for what you want to do though is that you need a two pole GFCI to protect a multi-wire branch circuit, and those only come in breaker form. However, there is no such thing as a double-stuff GFCI breaker to begin with, as the electronics required to make a GFCI work take up too much space to be fit into a single breaker package along with the two breaker mechanisms.
So, you'll need to put the GFCIs somewhere else -- this could be a "spa panel" placed inline with the circuit with a 2-pole GFCI breaker in it, or a pair of GFCI receptacles or deadfronts at the "end of the line" for the MWBC in that you would have to have the two "sides" of the circuit have separate neutrals from that point on to avoid confusing the GFCIs with improperly divided neutral currents. In this situation, you'll still need to use the DNPL152015 quadplex breaker in the main panel, as described above.