I use Bitwarden with a self-hosted Vaultwarden server, both on Firefox (Linux) and GrapheneOS. I'd say it works better than any other Android password manager you'll see. If you enable every single compatibility option in the auto-fill settings, you can even get it to auto-fill some very stubborn bank apps!
If I want to add a new account, here is what I do:
- Click on the Bitwarden auto-fill box that appears under the password field
- "+" in the lower right
- Enter my username, generate the password
- Save, click on it, choose auto-fill
- Done
I believe, that on iOS it's the keyboard/OS that generates the password for you, and not Bitwarden, but as I haven't used an iDevice in a few years, I may be wrong.