I received an email warning from Atlassian that user passwords won't be allowed after March 1. I followed the steps at this page to create an app password and apply it to Sourcetree (v. 3.4.7):
https://support.atlassian.com/bitbucket-cloud/docs/app-passwords/
I granted almost all permissions to the app password, except account/issues/wiki.
When I try to edit or add an authentication account in Sourcetree, it spins a bit and displays the error message: 'Your credentials lack one or more required privilege scopes'. I've tried both HTTPS and SSH, using Basic authentication. If I use my user password, it works fine (but of course that apparently won't work after March).