The big thing I'm missing most is LastPass. Without access to my passwords, I can see myself falling back to Chrome. In fact, I need to keep Chrome running so I can look up my login names and passwords there in order to copy them over to Bonsai when I'm being asked to log in. If you could support popular password managers inside your browser, that would help a lot!
You assume most people have the patience to copy paste passwords from Bitwarden rather than the ease of Lastpass - just doesn't work for 99% of the population.
I don't know about Keywarden, but KeePass just uses a global hotkey that can be used to type in your password in a context-dependent fashion (figures out the relevant password from the page you're on). No browser integration required, yet no UX hit. (Edit: But I have no idea if its "figure out what page you're on" functionality would work with Bonsai.)
A password manager integrated with a browser can offer more security, because it can verify the domain to prevent copy-pasting the password into a phishing site.
Having your password manager tied to your browser is more secure because the saved password doesn't show up unless you're in the correct domain, preventing phishing attacks.
The big thing I'm missing most is LastPass. Without access to my passwords, I can see myself falling back to Chrome. In fact, I need to keep Chrome running so I can look up my login names and passwords there in order to copy them over to Bonsai when I'm being asked to log in. If you could support popular password managers inside your browser, that would help a lot!