I been experiencing the same issue, if you go to Settings/ your Icloud name/ICloud/ Private Relay and turn it off this will fix the issue with Alexa App not having internet.
I notice as well that the following Apps not working correctly on Private Relay:
Unifi Network App
OKTA verification App
HotSpot (your devices from the phone)
Tesla App
iRobot App (was not working on 5G but on LTE was working now they fixed it)
ED7779
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