Zetetic Codebook [1] is the way to go.
Pros: • It has desktop clients • It has apps • It has secure encrypted sync • It has responsive dev team • No silly subscription model
Cons: • It doesn't have a fancy web app (but do you need one ?)
I've no affiliation apart from being a long term happy user.
> ...silly SaaS services like LastPass or Bitwarden?
...rather off-putting considering Bitwarden is nothing like LastPass in execution. For starters you don't need to pay for Bitwarden and you can run your own backend for self-host. Some of us use our password managers with others and would like to share things. I'm happy to pay for this feature.
So no, you're not required to leverage Bitwarden as SaaS like LastPass. They're not the same in that respect.
I have no affiliation with Bitwarden other than being a customer who dropped LastPass after the acquisition years ago.
In addition, there are open source alternatives that have all the features you mentioned (namely the Keepass/Keeweb family).