Hi loose rivets,
could you elaborate more? The issues you have show on a Windows 10 computer I understand.
When you try to "sign off from email to test the new password": You try to sign off from gmail? Do you try that inside any Internet Browser (which one), in a gmail app for Win10, In Office Outlook, in Win10 email app, ...?
Is your Windows 10 username set (linked) to your gmail-account name (that is, the email address of your gemail account)?