[Badge] Refactor Badge state managing logic

This CL fixes a couple of badge state related issues. First, it prevents the badges created before restoring instance states from being overwritten by the old instance states. Second, it makes badges reload their default style settings everytime when its being recreated so if the environment has been changed, the default values will reflect the environment change.

This CL also fixes that several attributes were not correctly saved/restored or their default values were not correctly loaded.

Resolves #2032

PiperOrigin-RevId: 420096508