I'm very happy to report that I received an answer from the Microsoft.
Seems to be a known issue with the Personal Gateway. In the meantime, we have a workaround available as below:
1. Open the On-premises Data Gateway (personal mode) desktop app on the machine where the gateway is installed.
2. Go to the connectors tab and switch off the Custom data connectors feature.
3. Click Apply -> Apply & Restart.
4. On the dataset page, click edit credentials and sign in.