It would be marvelous if the local app and the browser app would talk to each other to remember when they are logged in.

Perfect, open-source, multiplatform and secure

BEST password manager so far !

Clear, simple, easy-to-use.
Basic version allows you to get multiple device sync. for free ! (That's game breaking in the market)
But as many as other smart features.

And premium version is ~10€ / year, which is VERY affordable, that includes many security options, as for example TOTP (2FA).

Tried Dashlane before (which is good one too)... but I have strictly no regrets being part of Bitwarden community for 1+ year by now :)

Obviously, by default, one of the best password manager app available to us