Password Generator in iOS Extension

I would like to be able to use/fill from the password generator directly from the iOS extension rather than having to switch back & forth between apps. Maybe it could also record the URL (if applicable) that the password was generated for.

IMHO a better idea would be to allow adding a new site in the extension, like in desktop browsers

Does iOS even allow to do such things? I come from KeePass and the KeePass apps for iOS also all require you to copy the username and password to the clipboard, switch the app and then paste it in yourself. There is no auto-typing like on Android with KeePass2Android. I’m really missing this, but in case iOS doesn’t support it, there is no change for Bitwarden to support this.

The iOS extension for LastPass has a section for password, form fill profiles, and a sidebar to add or generate a new password.