It shouldn't even be that complex...
I might be mistaken, but ultimately a password manager is basically nothing more than a database of passwords in an encrypted zip file, right? That could entirely be self-hosted with off the shelf open source applications stringed together.
All you'd need is a nice UI stringing it all together.
Edit: I'm not sure why people are downvoting me. Is that not what a password manager essentially is?
I'm guessing they probably have rules against plagiarism, or passing off other people's work as your own.
So then I guess it would be down to whether using AI (without disclosure?) is plagiarism or not