Where then would the Mosquito fit ? a third type of tactical bomber ? or as a superior model of "heavy twin" ?
It's a final tier piston-powered fast bomber/fighter.
The 'fast bomber' type fits dornier (2)17s and Ju88s to a 'T', too.
And then there's how to fill out the research of the different types, even with paper or failed projects, there's not always enough distinct types of aircraft to populate the tech tree.
Well, the way I do it is to have the main techs be (single engine) light bombers, fighter(-bomber)s and carrier airplanes, (twin engine) fast airframes and medium bombers and heavies just one class. Then, for each tech, there are subtechs for the individual types, such as (for fast airframes) heavy fighters, fast bombers and twin-engined torpedo strike. Each tech costs ~half what the vanilla full tiers do, so that the whole lot costs more or less the same (but the choices are slightly different around combinations). Research single engine fighters and you get nothing new, per se, but it opens up both fighter and fighter-bomber (and night fighter, when/if there are options to support radar effects for night flying plane models) models. I think it works pretty well.
If there were to be a design system similar to the MtG ship one for aircraft, you could do it more-or-less similarly. Main tiers would be engine models and the "subtechs" would be airframes. This reflects the way 'plane development went, with new, more powerful engines making less draggy, more speed-adapted airframes more worthwhile to develop, leading to heavier armament (because they realised that the time windows for firing would be shorter, so that more "punch" would be required). A slight complication might be radial vs inline engines, but you really would want to include both because the relative benefits and issues are significant and strategically interesting.
I think perhaps too, that advances in rockets, bombs and air-dropped torpedoes, could be modelled as distinct technologies, so that e.g. naval strike doesn't necessarily go up with the aircraft model, but by the weapon techs.
E.g. tac bomber 1, has the stats naval_strike_attack = 8
while tac bomber 2 has the stats naval_strike_attack = 12
so, instead of that being the case, then it would be "armour piercing bomb" tech, to give tac bombers +50% naval strike.
Yep, this is more-or-less how I have handled torpedo carrying naval strike aircraft, although I will note that development of doctrine and alternative/complimentary weaponry had a role. Unguided rockets as both flak suppressant and anti-(unarmoured)ship weapons are particularly interesting. Guided bombs and rockets are interesting, too, of course, but arguably a different category, not routinely used with torpedo strike units, as far as I know.
The "light twin" already exists in game, it is the "Heavy Fighter", see the wikipedia article on Blenheim, no-where it says it is a "Medium Bomber", it is classified as a "Light Bomber / Heavy Fighter":
https://en.wikipedia.org/wiki/Bristol_Blenheim
So we can keep things simple: No need for even more aircraft types, and make the Heavy Fighter which is currently very niche into something more useful, by giving him a medium Naval attack capability and a small "Ground attack" stat.
Take a closer look at the Blenheim subtypes. The bomber versions were totally different in detail to the fighters, with different nose structures, different internal arrangements and such. The base airframe was the same, but you either made a bomber or a fighter; the same 'plane couldn't do both. It's the same deal with Ju-88s - they could be fitted to take torpedoes, schrage musik, etc., etc. - but you didn't have one 'plane with the "organ cannon" mounted AND bombs AND brackets for torpedoes.
Treating them as subtechs, similar to carrier planes in vanilla, works well, though - it allows cheap conversion of one subtype to another, but not wings that can do everything without conversion.
Which strat bombing stat values exactly do you propose for the 4 TACs and 3 STRs?
I actually have an exra "early" layer, so one added tier, and use the following:
Medium-X = 7
Medium-0 = 10
Medium-1 = 12
Medium-2 = 15
Medium-3 = 16
Fast-1 = 10
Fast-2 = 12
Fast-3 = 14
Str-0 = 24
Str-1 = 28
Str-2 = 32
Str-3 = 36
These fit the low end of historical models; it's worth noting that your first variant for each model in WM is "free", so these values will almost always be adjusted a bit by the initial variant, generally to be a bit higher. (The variant received varies by nation - nations that never created such a model get either a default "average variant" or some xp to design one - which is always a choice for the player, anyway).
If you want to see the full stat set let me know by pm and I'll link you the (somewhat convoluted) spreadsheet I use.