If I launch the client without steam open it works fine, if I then load steam I get the error, if I then close steam the error remains, but if I close both down and only have the client open it works again.
You only actively get logged out when there is a failure to refresh your access token. We have to log out then because we can't use the API fully until you reauthorize.
Your steam account name can be different.
If you can't login to steam for resetting password, you will also not be able to link any new account to steam even if we delete the old account. So fix your steam account first.