Kara lived the first part of her life entirely unaware she had once been someone else. but, after failling to escape from krypton, the trauma of getting trapped in a ship makes her fully remember her previous life.
Now she must strugle with two sets of memories and make sure her little cousin is gonna be ok, knowing everything the DC universe can throw at her she knows even being a Kryptonian won't be enough.
The world is mostly Young Justice but I won't deal with the team all that much.
MC has the memories of a young guy from our universe but she was trully reincarnated and has lived most of her life as Kara Zor-El without any memories of her previous life. It's best to think of it like an amnesiac who has built a new life suddenly remembering his past memories.
There will be Smut but only MUCH later in the story and it can be skipped.
WARNING! Kara isn't above killing her enemies, but she WILL avoid doing so when it doesn't put anyone else in danger and the villain isn't someone like the Joker.
If she is fighting the Joker and she gets to him before anyone else... well accidents happen.