Firefox logging out my accs from web every update

Is it only after an actual update, or after any restart per se?

Only after actual update

Theoretically during major version updates once a month the user agent identification changes, so if those sites track the browser fingerprint paired to the claimed session it might see the discrepancy and request new logins. That however should not happen during minor/patch version updates every week within the cycle, so this theory would only apply if you don't update frequently, and only see this exhibit on the major bumps.