Frankly it is beyond my understanding how simple login issues with native bitbucket account can be such a problem in Windows version of Sourcetree for so long. I was using Sourcetree on MacOs and Windows and while MacOs version is ok - Windows version is a constant disaster all the time since basic auth (login+password) was deprecated. Oauth constantly require "reconnect" and frequently - even after reconnect - it is not working anyway (asking for password, and ignoring it silently). I finally moved to use AppPassword (API tokens, to be correct, see below) and simply failed to make it work at all - after hours of reading threads and googling. Clearing caches, clearing keystores, reinstals, tweaking repo options to bitbucket account etc etc - nope, Sourtree still asks for login/password, makes trash records in keystore, ignores your input and still fails despite ANY password enetered (account/app). I tried full set of combinations of factors like some old-school Sierra quest. It simply not work.
Installed GitHub desktop - poof, instaworks with simple login/app password (api token) setup, zero questions asked. Goodbye Sourcetree, my expectation was not high but this is insane.
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For anyone googling "How to solve login problems in Windows version of Sourcetree" - for the sake of your sanity do not spend time "solving" it, switch to anything else (i switched to GihHub Desktop with zero problems). Clearing caches in LocalAppData, Resetting windows keystore, reinstalling and trying different passwords will not help you. As well as support will not help you - all their advices can be summed up to "turn off computer and turn on again and try over"