Addresses ENG-8602. We want consistency on all password inputs; otherwise, the user will end up with a different string depending on which input they used. I think the mismatch between LegacyRegisterPanel/LogInPanel is contributing to user reports that they forgot their password, or that the password doesn't match up anymore.
A better solution here would be to try to factor out all password inputs in our app, but I didn't have time for that given our launch schedule this month.