I have the same issue and the browser console is showing this error:
Access to fetch at 'https://api.minecraftservices.com/minecraft/profile' from origin 'https://www.minecraft.net' has been blocked by CORS policy: No 'Access-Control-Allow-Origin' header is present on the requested resource. If an opaque response serves your needs, set the request's mode to 'no-cors' to fetch the resource with CORS disabled.
Seems like this would be a simple fix for the Minecraft team- just add the Access-Control-Allow-Origin header to your API response.
Any idea when this will be fixed?