I have no idea what I did, but after factory resetting the phone, I was able to log in and start downloading the first-party apps. I’m also able to enable Developer mode and everything.
Again, big thanks to olf and especially lpr for all the help and effort they put in and for not giving up!
We didn’t exactly solve the original issue of the SSL handshake, but I hope this would be useful to someone else. Who knows, I may encounter the same issue in the future…