Whatever password manager you use I would consider browser integration critical. This is because it will check the domain for you and prevent phishing attacks that may work if you need to copy+paste your password. The fact that the password doesn't auto-fill is a huge red flag that interrupts your regular workflow and requires an unusual manual action to be phished.

But whether that is an in-browser password manager or a third-party manager with browser-integration (usually via an extension) probably doesn't matter much.