The Bitbucket cloud REST API does not support branch creation / deletion. However the REST API for Bitbucket server does as found in the link below:

https://developer.atlassian.com/static/rest/bitbucket-server/4.3.1/bitbucket-rest.html#idp2564976

Use case: we want to standardize and automate the branch creation process and would most prefer to do this via the REST API. Delete would be nice too.