There is an irony in password managers that stores your password but need a password (passphrase would be better). A password for your passwords. Fundamentally this is because the only secured space, only you can get in and no one else, is your own brain.
Most password leaks are usually caused by bad implementations on the server side. I have an authentication protocol to avoid many password leakages I’d like to share one day (double salt, one from client, one on server so password is never shared to the server).
If your computer is compromised whatever token/cookie you will get from the authentication will be also compromised.
Assuming the computer is compromised also open a lot more issues, privilege escalation can be done in a lot of ways depending of what is being installed (even sudo was hit by such issues https://www.cve.org/CVERecord?id=CVE-2021-3156 )