How do I sign-in and access my HBO NOW subscription?

HBO Max requires its own app, separate from the Apple TV app. The Apple TV app on third party streaming devices will only support the iTunes Store, Apple TV+, and Apple TV app Channels. That excludes any services that requires their own app. The Apple TV 4K box offers much more than the Apple TV app on a smart TV, and in this case that applies to third party apps, and how the Apple TV app is able to interact with some of those apps on an Apple OS (iOS, iPadOS, tvOS).

Which devices work with HBO Max? - HBO Max Help Center

Until HBO Max becomes available in the LG Content Store (if at all), you will not be able to stream HBO Max without an external streaming device. Maybe use AirPlay if your TV supports that. You may want to connect your Apple TV 4K again.

HBO Now is no more. HBO Now has transitioned into HBO Max, since May 27, and that is completed per June 12.

HBO Now required its own app, separate from the Apple TV app.

If you had the Apple TV app Channel HBO, then that is different from HBO Now. If you had Apple TV app Channel HBO, then possibly you may continue with that, but I don’t think they take new subscriptions anymore.

HBO stops participating in Apple TV Channels, users directed to HBO Max app - 9to5mac.com