Bitbucket has, as of 5.4.0, a better webhook integration.
This is especially good for the Bitbucket users that can't install unsuported plugins. The new solution is always enabled and doesn't need additional configuration.
The different payloads it has : https://confluence.atlassian.com/bitbucketserver/event-payload-938025882.html
I believe there isn't a webhook api yet, and I haven't found anything yet about plans of creating it. I think we have to wait until then?