To my knowledge, it's not yet known why this screen sometimes appears. I think rebooting / updating is a good fix for it. It seems to have started around the Switch 2's release.
The browser does have checks to sometimes ensure it's on the latest Switch version, but the "This feature is unavailable" screen seems like it's a new/different (or even enhanced) mechanism from that.
I'd also recommend trying to connect normally without the DNS, eg. on Automatic or Google DNS (8.8.8.8) once, to allow the console to "phone home" and verify that for itself that it's up to date.