No, it did not contain any specific port configuration (it could be listed under the ‘server’ key).
That reminded me that Octoprint has some cli-tooling of itself. And sure enough:
octoprint config get server.port returns 5000.
Similarly, setting it with octoprint config set server.port 5001 and running dietpi-services restart octoprint enables octoprint again on port 5001.
I could mark this as ‘the answer’, but I don’t think that restoring a backup should set a different server port? Perhaps DietPi should do something so that even after restoring a back-up octoprint is still available on the 5001 port as mentioned in the documentation?