Apple ID changed, my phone’s (soon to be) bricked?

hi all

for Some time, my family has shared an apple id, though we sometime last year decided to stop doing so. However. I hadn’t signed out of the original from iCloud on my device, and had find my device on. And then my sister changed the ID email and password. Which for those who can’t recall, means my phone is now stuck in a limbo where it wants to log into an id that doesn’t technically exist, though changing it back and logging out has been known to fix this issue. But then she promptly since has forgotten them, lost access to the phone used for password recovery (seriously, I can’t make this up) and the email wasn’t hers to begin with. So basically, my data is gone or stuck on this phone, right? I’m trying to transfer my data to a new phone I just got. For various reasons I can’t use a computer as an intermediary and for said reason stated before I can’t use iCloud. But surely if I use quick start to migrate my data I’ll also migrate using the scuffed log in and just give myself a new $1200 brick on top of my old one? Since quick start uses your “main” Apple ID login, which in this case is the one I can’t log out of. I’m just trying to see if anybody has any other possible solution to this I could try. Or if I’d be able to maybe use quick start without migrating my scuffed login and being able to use my actual apple

id, which on this phone is used for the App Store and iTunes Store, so all of my purchases are from it. Thanks for any advice y’all can give