Bitbucket 9.4+ requires users to provide their password when updating their email (i.e. through the "Manage account" page, or through REST/API). Admin operations that change a user's email (e.g. editing a user through Admin page) are unaffected.

To disable this feature (and thus not require the password for user email updates), the following should be set in $BITBUCKET_HOME/shared/bitbucket.properties:

feature.enforce.password.user.email.update=false 

Then, restart Bitbucket for the changes to take effect. If you run a Bitbucket cluster, a rolling restart is enough to pick up the configuration properties you set to enable the features.