I have the exact same problem you described. Mac Pro M1 (Ventura 13.2). It doesn't sync my passwords and logs me out everytime I quit Opera. Uninstalling, cleaning and re-installing does not work, Dev build does not work. On Windows 11 everything works perfect.
I have the same problem with Opera 95.0.4635.37 on W11 22H2 22621.1265
the few websites where I used auto login in Opera now keep requesting log-ins every time,
sync no longer works and when trying to access https://auth.opera.com I can't even log-in.
requesting a password reset does not result in an e-mail and trying to re-register the same username results in an error as the username is already taken.
funny thing is, using the very same account not working in Opera desktop still seems to work in Opera on Android so I suspect them having issues with their logon servers.