Do you have a complete and functional Apple ID account already?
If a new Apple ID account is created on a smart TV or third party streaming device, then you may be asked to complete the activation on the web at: activate.apple.com.
Apple IDs for subscription services need full name and user details as asked, a verified email address (respond to test message), and a valid pre-authorized payment method (even for free trials, so that it can auto-renew when not canceled).
How to create a new Apple ID - Apple Support
Manage your Apple ID - Apple
Add a payment method to your Apple ID - Apple Support
Apple ID support - Official Apple Support
When signing in on a new device with your Apple ID account, you may be asked to enter a verification code for two-factor authentication. This verification code will be send to a trusted (personal) Apple device (as pop-up notification), or to a trusted phone number (as text message), as you may have selected for your Apple ID account.
Two-factor authentication for Apple ID - Apple Support
Get a verification code and sign in with two-factor authentication - Apple Support
When using the Apple TV app, you can sign in to the app through the in-app Settings (sprockets wheel icon), using the Apple ID account that has the subscription.
Get Apple TV+ - Apple Support
Apple TV app user guide for smart TVs and third party streaming devices - Apple Support