@burnout426 Thanks for your reply. I managed to solve (I think!) this problem - I mean, make it disappear totally - yesterday by... switching to another browser, here is how.
I was so frustrated that I indeed switched to MS Edge. I'll spare you the details of the migration, but I soon found out that Edge too was "forgetting" the credentials I was entering once I would close Edge and reopen it.
It became clear that the problem was not just Opera"s, but a system wide one (and it connected with the odd fact that another program, not a browser, had lost the credentials it had had for months. So I tried various ways to fix the Windows Credential Manager - to no avail. I ended up running the DISM command - which didn't find any problem - and then SFC, and it reported having found some problems and repaired them.
And indeed, now Edge doesn't forget the credentials I reentered for a variety of sites. I suppose - haven't checked - that Opera does too, and will now check that other program too, and will stay with Edge as my default browser.