Password managers could take over and manage cookie storage/retrieval.
Or browsers could treat cookies more like passwords and have a user-controllable flow on each new session: "Here's this site's cookies from your last session, do you want to place these back in the browser storage?"
The fundamental issue is that browser cookies and password managers have an overlap in their usage domain.
not all of my passwords are for browser-based services, not all of my secrets are passwords, and I have several devices with different operating systems.
(eg, my password manager includes github recovery tokens, ssh keys and passphrases, recovery questions, my tax and health service identifiers, wifi passwords and the admin passwords)
Or browsers could treat cookies more like passwords and have a user-controllable flow on each new session: "Here's this site's cookies from your last session, do you want to place these back in the browser storage?"
The fundamental issue is that browser cookies and password managers have an overlap in their usage domain.