you should always delete all cookies on browser close, there’s a setting to do this automatically. also never accept 3rd party cookies. if you want convenience of easy logins save the passwords into your browser
Its about surface area. A password manager that has no browser integration is by its nature less likely to be compromised, as there are far less vectors of exploitation.
Don't store your passwords in the browser. Use a proper password manager. How its gets from PM to B is up to your risk appetite.
the browser password managers are good enough for most uses