As to the current situation, I get the following, maybe it helps for debuging:
macmini:test$ xcrun notarytool history --keychain-profile "my_profile" -vvvv
[10:22:32.154Z] Debug [MAIN] Running notarytool version: 1.0.0 (21), date: 2022-05-24T10:22:32Z, command: /Library/Developer/CommandLineTools/usr/bin/notarytool history --keychain-profile my_profile -vvvv
[10:22:32.167Z] Debug [KEYCHAIN] Attempting to load Keychain data for profile name: my_profile
[10:22:32.180Z] Debug [KEYCHAIN] Found Keychain password item "my_profile" with ID XXXXXXXXXX:YYYYY.
[10:22:32.187Z] Info [API] Initialized Notary API with base URL: https://appstoreconnect.apple.com/notary/v2/
[10:22:32.188Z] Info [API] Preparing GET request to URL: https://appstoreconnect.apple.com/notary/v2/submissions?, Parameters: [:]
[10:22:32.189Z] Debug [AUTHENTICATION] Delaying current request to refresh app-specific password token
[10:22:32.191Z] Info [API] Preparing GET request to URL: https://appstoreconnect.apple.com/notary/v2/asp?, Parameters: [:]
[10:22:32.192Z] Debug [AUTHENTICATION] Authenticating request with Basic Auth. Username: YYYYY, Password: private, Team ID: XXXXXXXXXX
[10:22:32.195Z] Debug [TASKMANAGER] Starting Task Manager loop to wait for asynchronous HTTP calls.
[10:22:32.938Z] Debug [API] Received response status code: 500, message: internal server error, URL: https://appstoreconnect.apple.com/notary/v2/asp?, Correlation Key: RFD32TYXONHX7XXXXXTWFTT5RQ
[10:22:32.939Z] Error [TASKMANAGER] Completed Task with ID 2 has encountered an error.
[10:22:32.940Z] Debug [TASKMANAGER] Ending Task Manager loop.
Error: HTTP status code: 500. Internal server error. Error communicating with authentication service. Please try again at a later time.