Report with Power BI dataset as data source can't be refreshed online

I have set a Power BI dataset as the data source for a report ("DirectQuery in AS - Power BI dataset"). The report is working fine in desktop and can be refreshed, but I am not able to refresh the dataset using Power BI Online. I get the error message:

Something went wrong
Refresh failed because this semantic model requires a gateway. Please select a gateway from semantic model settings.
Please try again later or contact support. If you contact support, please provide these details.

Activity ID: e01090c0-6dd5-44c0-85de-6e7bcb516ee6
Request ID: 34c290c2-2702-5a5d-7a0e-7f97049a3f8e
Correlation ID: 34caef49-389b-1a9e-e6cc-915b1f021b61
Time: Tue Nov 28 2023 07:56:40 GMT+0100 (Mitteleuropäische Normalzeit)
Service version: 13.0.22007.81
Client version: 2311.1.16680-train
Cluster URI: https://wabi-europe-north-b-redirect.analysis.windows.net/

If I then try to select my "Personal Gateway", I get this error message:

Something went wrong

Failed to use the selected gateway. Please make sure the gateway is up and running and try again.
Please try again later or contact support. If you contact support, please provide these details.

Activity ID: e01090c0-6dd5-44c0-85de-6e7bcb516ee6
Request ID: 6a116dcf-e5ec-dada-b654-b25b3aebe8d8
Correlation ID: f6b72bde-e02f-7c0d-a608-404580efbbfb
Status code: 400
Time: Tue Nov 28 2023 07:57:49 GMT+0100 (Central European Standard Time)
Service version: 13.0.22007.81
Client version: 2311.1.16680-train
Cluster URI: https://wabi-europe-north-b-redirect.analysis.windows.net/

But I don't understand why it needs a gateway at all? And how could i fix this problem?