I'm currently using username + password to push to a Bitbucket repo with no major issues so far.
Atlassian have said, however, that on 1st March 2022, "you will no longer be able to use your Atlassian account password when using Basic authentication with the Bitbucket API or Git over HTTPS. For security reasons, we require all users to use Bitbucket app passwords."
I've gone in and created an app password for PowerApps (with full access permissions). However, when I try to log in with it, I receive the error message "Invalid username or password. Please try again."
Does PowerApps not yet support app passwords?