These are backstories. If the pact changed you into a magical being, that's same as sorcerer, if it allows you to channel power from an entity, that's cleric, if it gave you access to secret knowledge of magical formulas, that's a wizard. It matter what you are, not how you became that!
Of course it matters how you became that. That's
literally what a hero's journey IS.
Furthermore, I think "Faustian pact: the class" is a bad idea to begin with. It places the pact in the most boring place it could be: in the character's past before the game even begins. Powerful entities tempting characters with power is cool concept and something that is interesting to explore during the play, but as we now have determined that such pacts grant warlock class, this limits their utility in play.
But it must go there. There is no other place for it to go. That's the inherent problem of the Faustian bargain, it is always with an entity that has all the cards.
If it were something to be written by the DM, with every trick in the book,
no one would ever play it, because players aren't stupid, they don't sign their (game) lives away for stupid and $#¡††¥ reasons. I doubt most DMs would even
want to, since that is even moreso heavy lifting, putting a ton and a half on thr DM's shoulders. You'd be effectively banning the class. (But perhaps that was the intent all along?)
Besides, the actual story (and tragedy) of Faust is everything he does
after the bargain, not before. The bargain is the most boring part of the whole thing, mere signing of a form. Being saddled with the
terms, straining against limits, either paying comeuppance for hubris or (in more positive tellings) achieving an underdog victory, managing to outwit or outplay a coercive power and genuinely beat them. Both of those are compelling narratives. They have
jack-all to do with being a D&D Wizard or Sorcerer.
Both classes to do both. The origin stories are fungible.
No, they don't; and no, they aren't.
The "pact" you describe with this dragon is nothing. It is not a pact. It is, at best, a
sale. A one-time, completed
transfer.
Likewise, your "inherited" Warlock pact
isn't even a pact. The whole point of the Warlock is that a contract requires the participants to
willingly accept it. A contract without that initial consent literally ISN'T a contract; even the most twisted devils recognize
that.
(Though, in fairness, most D&D devils are outright idiots constantly destroying their own reputation...so it's not like they are exactly paragons of rationality here.)