But that's helpful for the 99% of Chrome users who aren't technical enough to even know that they should be using a password manager. Having a halfway-decent password manager "just work" when they "open the Internet" is still a huge plus.

Why? Chrome has had a built-in password manager for years, synced to your account, and accessible on the web: https://passwords.google.com

And it doesn’t work! It breaks on several websites I use routinely (e.g. my credit union). As far as I can tell, browser password management is a dirty hack. There is no real “login API” that could be used to build a proper password manager.

It works fine for millions of people and websites. What exactly is the issue you're running into? All the other password managers use browser extensions to do the same thing Chrome does natively.

There is the Web Authentication API: https://w3c.github.io/webauthn/

It asks before storing passwords and, in case of generated passwords, also displays the password - so it seems okay for me. Or do you think it's a lock-in because of missing export options?

Exporting passwords from Chrome:

https://support.google.com/chrome/answer/95606

"Export: To the right of "Saved Passwords," click More : > Export passwords"

It's a lock in because people using this won't even know their own passwords.

Why would it be more dangerous than any other password manager?