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.
Ease of Lastpass is the same as ease of Bitwarden, both have extension for browsers :)
And now we’re back to the original commenter pointing out that this new browser lacks such extensions
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.
Browser without extensions is like bike without wheels.
All those ads and javascripts...
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.
Plus the password doesn't transit through the copy buffer, which is probably less secure