Currently, if you have the "Allow automatic merge when builds pass" branch permission checked when you merge a PR on the UI, it will wait for the last build to be passed before the PR is merged.
However, if you use the API 2.0 endpoint below to merge the PR, it does not wait for the last build to be passed, it will merge the PR straightaway.

POST /2.0/repositories/{workspace}/{repo_slug}/pullrequests/{pull_request_id}/merge

API Reference: https://developer.atlassian.com/cloud/bitbucket/rest/api-group-pullrequests/#api-repositories-workspace-repo-slug-pullrequests-pull-request-id-merge-post

Feature request:
It would be useful to be able to use the same PR /merge API 2.0 endpoint that honors the auto-merge branch permission feature.
Alternatively, create a new API 2.0 endpoint.