Around a week ago the update checker stopped working. Not sure if this is something caused by a backend change on the side of modrinth or something else.

The underlying issue is indeed on Modrinth's side; modrinth/code#1045 can be used to track the issue. Since the API is just masquerading the response as if no mods need updates, Mod Menu cannot do anything to solve the issue. I'll keep this issue open until the underlying issue is resolved.

我也遇到同样问题，

The underlying issue seems to be resolved as per an announcement in the Modrinth Discord announcements channel.

so its up to modrinth to fix this? have you guys reached out to them?

Yes