Does Apple TV manage your subscriptions to services like HBOmax, netflix, Disney, ESPN, and Discovery ?

That depends on what you mean by "manage".

You can access your subscriptions on an Apple TV, watch content from them and you can view and cancel them on the Apple TV if they are paid through your Apple ID, if that is what you mean.

Link-> Manage subscriptions on Apple TV - Apple Support

It won't have any way of cancelling subscriptions you obtained directly from the providers website or on an App on a non-Apple device however, but you can still access them though their apps and watch content form them on an Apple TV.

In that case, no. If you have subscriptions to their stand alone apps, then you must use their stand alone apps to access their content.

If you subscribed to a channel for one of those services inside the Apple TV App, then you can view the content for that channel inside the Apple TV app, but unless otherwise noted by the content providers you cannot use the channel subscription on their stand alone app.