Thoughts on if Damian had been a girl:
Worst case scenario:
Talia and Ra’s make no secret of the fact that they’re disappointed she’s a girl. She has all of Damian’s training and an inferiority streak a mile wide. She’s not revealed to Bruce because she’s not seen as valuable leverage, and she has no interest in her father because she sees him as weak. Until Cassandra defects. She sees that as betrayal and asks to be the one to take her down but when Bruce Wayne announces he’s adopting Cass she snaps. She’s doesn’t just try to kill Tim: she succeeds. Damia* becomes Cass’ unhinged nemesis.
Medium case scenario:
Talia wants Ra’s to accept Damia as his heir. When he refuses she starts questioning her own internalized misogyny. She decides to make Damia her heir and the League is split into two different factions (like it was so cohesive before). Damia is dangerous but less egotistical than Damian because she doesn’t get the insane hypermasculine primogeniture shit from Ra’s. She occupies a lot of moral grey area like her mother but perhaps ultimately has a similar arc to Damian, being a part of the Batfam, but on her own terms.
Best case scenario:
Talia sees a daughter as useless in her father’s crusade and in her attempts to manipulate Bruce and drops Damia on the manor doorstep as an infant. Bruce gives her as normal a childhood as possible. Alfred strategically refuses to do night feedings and diaper changes at his age and Bruce is forced to step back from the cowl (because they can’t really bring in a stranger to nanny and everyone they know already leads a full double life). The family thinks this is brilliant because Bruce was getting older and was riddled with injuries. Also they love Damia and spoil her rotten.
Anyway, those were my morning commute thoughts.
*Not tied to that name, it seemed like convenient shorthand. Also, it means “untamed” whereas Damian seems to mean “one who tames” or at least that’s what cursory googling tells me.