Bitbucket Cloud currently lacks feature parity with Bitbucket On-Prem (Server/Data-Center), specifically for the ability to enforce a pre-receive hook that verifies that the user performing a push is exclusively pushing commits written by themselves, and not another user.
This can also be useful to enforce that any commits written are written under expected committer details (username/email) that match the authenticating user account and not an unaffiliated account.

Ref: "Verify Committer - rejects commits not committed by the user pushing to a repository."
https://confluence.atlassian.com/bitbucketserver/using-repository-hooks-776639836.html#Usingrepositoryhooks-Defaultpre-receivehooks