Experience Shell throws error - yet running actions directly without the shell works fine

I had this problem quite a lot of times while testing my App Builder Application.
Basically I always first tried to run the actions via the Experience Shell yet run into problems because of it regularly.

(aio app run)
The error always looks like that with different "code":

time: 874 ms

failed request to 'https://#####.adobeioruntime.net/api/v1/web/#####' with status: 400 and message: {
"code": "lozU6fbz5Ms2dlzFrIRhSyPMm1J7kjNO",
"error": "There was an error processing your request."
}

Strangely everything is still working when testing without the shell using f.e. Postman or Altair GraphQL Client. Even directly calling an action in the browser works.

Any idea why that error happens and/or how to solve it?
(I am using Chrome browser and sometimes clearing the cache seems to help)