reading the post you wrote sounds like fan fiction but it's very ya-ho games story telling with the convoluted plot twists and shit and overcoming impossibility with miracles and some shit. Aisha (protagonist of the 3 games of Barony games) is a "negative luck" character. Every game setting she seems to get into random shit due to her abysmal luck, but also due to the luck being so down in the negatives, it loops back into the positives and she somehow overcomes all 3 games and survives (probably canon virgin endings too since every game she starts as virgin). Even though the games have a chronological order of release, the dev stated that each game is standalone, and no set-timeline of when things happened. There are barely any references to other games, and the game timeline can go either way (it could start from 1, 2, or 3rd game). Some endings she becomes too OP (like slaying a dragon and dragon's are very strong in that world, it's like a single person killing a tank IRL with not much combat experience). Or even being too rich that she doesn't need to explore/work anymore. Basing on the other games setting then the logical conclusion would be that the default ending for each game would be the virgin ending (where there is not much change to her status quo other than surviving her extremely bad luck and killing the big bad of the game).Welp, the Claire game is confusing, to say the least. The timeline is somewhat messed up, too. Anyway, I'll recap the whole storyline incase you don't want to play that headache-inducing game but still wants to know what happened:
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It would not be out of character for her to be whisked away to another world to fulfill another task/job (did not know she appeared in that game since she has no sprite/picture in the CG in hitomi la for claire).
Guess the hat guy just likes helping fem protagonists and did not appear in this game due to the canon protagonist of this game being male lol.
The timeline between cecilia to jacko is vague, since if the time between games is so long, then why is the huntress of tequilla (the one who gave the house to cecilia) still young and does not appear to have aged. Tequila also IIRC did not appear in the cecilia game, but there are many hints/misdirections as to the identity of tequila in that game. There are many blonde women in that game that was suspected to be tequila but proven false/ not conclusive enough (one of them being cecilia's real form, another is the child that turns out to be a big bad in universe). It has been established that tequila is great at disguising but her primary features mostly remains (blond hair). It's very questionable how eating the food she was given here turned her from old tequila to young again (and she does not have a unique portrait/picture). Might be the dev just putting a joke scene, might be that the food is so good that she broke disguise.