Important note!!! Due to removal of compatibility with old version passwords in this version... ... !) user - removed insecure password storage; ... I still can't see any API-related warnings in the release. Just to be sure that you can understand my point: 1. Removing compatibility with old versio...

There is already important note due to removal of compatibility with old version passwords. Third party software should have been fixed long time ago ,new authentication method was introduced back in May 2018. Sorry, can't see anything about deprecation of old-style authentication both in the chang...

Yes, make sure you are using new authentication method. I think that a proper warning about deprecated API authentication with this release was at least essential. Problem is that I have a strange success/fail API authentication entries in the logs even after downgrade and restoring the last backup...

Make sure your PHP code is using new authentication method:
https://wiki.mikrotik.com/wiki/Manual:API#Initial_login

Have same issue with upgrade to the new 6.45.1 firmware.
API authentication fails, and same is working with 6.44.3

Is it related with removed unsafe user passwords storage?

Same here, can't login after upgrading both using WinBox and MAC telnet.
Only can connect using SSH with public key auth configured.