The error message is actually the Home Assistant Supervisor claiming that your browser isn’t presenting the cookie that verifies you’re logged in to Home Assistant.
I don’t know why this would cause problems, but turning it on is the only thing I’ve found that reliably reproduces the problem.
I’ve been testing around with different browser configurations, and I’m pretty sure this “401: Permission Denied” issue only affects users of Firefox who have it set to automatically delete cookies when the browser closes.