I have the following initial situation:
Goal: Every push a developer does in a branch of this project should trigger the scan for new branches in Jenkis and the build process for new branches or those where something has changed.
I have found the problem/solution. As I said, my Jenkins runs in a Docker container and is hosted locally on my PC (localhost:8080).
Through the credentials, the path from Jenkins into Bitbucket worked and so did creating the webhook. However, for this webhook, the Bitbucket server plugin entered its address (localhost:8080). So now when a push into a Bitbucket repo happens, this webhook was triggered on Bitbucket's localhost:8080 (so presumably Bitbucket itself and not Jenkins).
The solution was now quite simple. I used a tool called ngrok to make my localhost:8080 (on which Jenkins runs) accessible via a URL from the internet. I then only had to store this URL in Jenkis in system configurations and adapt the webhook in my Bitbucket repository.