As far as I can see a possible problem with webhooks and the gitea plugin is the usage of ssh credentials for gitea with a different url. AFAIK, the webhook checks only the html url in the payload of the webhook:
In my case the https (html) and ssh url are different. The scm event was triggered but the event matcher will not find any matching jenkins job for the webhook. However, the return will be 200 and processed.
You can test this with replacing the html url in the json, which gitea provides in the webhook view, and using curl to POST the request. If I inserted my ssh url in the html of the json, then the webhook triggered the job correctĺy.
Entering an alias in the jenkins settings does not change the way, the event matcher works. I don't want to setup a specific jenkins user for gitea as I wanted to use deploy keys only. Another solution would be to add a check in GiteaCreateSCMEvent.isMatch(..) with the ssh url: ...(getPayload().getRepository().getSshUrl());...