Are you actually concerned with your account setting files, rather than the launcher login credentials?
Those are saved off as ‘profiles’ that you can back up and then re-associate with individual accounts after you re-install. Instructions are here:
CCP will always require players to re-authenticate login credentials after a re-install, as permitting carryover is far too risky from a data security perspective. Even if you copied over the file housing those credentials, CCP would recognize that the launcher ID and token do not match and force a re-authentication process.