from the output of gcloud alpha logging tail --log-http

You can see that, only a GRPC call is made. Thus this tail http API seems to be invalid, and only GRPC works.

Initializing tail session.
=======================
==== request start ====
method: /google.logging.v2.LoggingServiceV2/TailLogEntries
== headers start ==
authorization: --- Token Redacted ---