HBO/HBO Max/Max through Apple TV app in-app Channels has been discontinued since mid 2021 [1], with more than a year prior of just catering to existing subscribers [2]. You’ll have to watch the Max in the Max app now.
Subscriptions as started in third party apps on Apple devices, may not be available on third party devices (unless those content providers have made provisions to extend it beyond the platform of the subscription). To be able to sign in on any device/platform, users should cancel and resubscribe with Max directly.
The Apple TV app on third party devices (such as LG TV or Google Chromecast) doesn’t offer Max content directly, nor does it offer that external apps “connect” to the Apple TV app for inclusion of content in Watch Now, Up Next, or Search. That latter functionality requires special support from the OS/platform, thus only on Apple devices (Apple TV box, iPhone, iPad).
Apple TV app vs. Apple TV box - Apple Community