The Apple TV app on the Apple TV box would recognize the Apple TV+ subscription from the Apple ID account as set active for the device. There is no separate sign-in for the TV app alone on this Apple device.
Settings﹥Users and Accounts﹥…
If it was already set up with a different account, then you can add a secondary account, and switch between the two via Control Center. Or group both accounts into a Family Sharing group.
There is no Apple TV+ app on the Apple TV box. Apple TV+ is a channel and tab within the the TV app.
Apple TV user guide (tvOS) - Apple Support