That's strange. The Elastic user should definitely work.
That message comes from kibana/index.tsx at 9d662b77bec867247421376ecb60a07202ed45f9 · elastic/kibana · GitHub which is a page I find hard to reach even in local testing.
It calls api/monitoring/v1/check_access (kibana/check_access.ts at 0bd772432a313599656d8fe8adfdc7e6ef5d328a · elastic/kibana · GitHub) on kibana so it could be that API is failing for some other reason and the UI is treating it as an authorization error.
If an exception gets thrown there it should show up in your kibana logs when you try to load the monitoring UI, so I'd recommend checking there next.