The offer should be redeemed in the first 90 days after setting up the new eligible device, else the offer expires.
The offer should be redeemed on the new eligible Apple device, in the TV app. The redeem button should appear there. No use in trying to redeem on a different device.
Read here how to redeem: Apple TV+ offer - Apple
Read here about the conditions: Apple TV+ offer - Terms and conditions - Apple
Read here if you have trouble redeeming: If you can't redeem your promotion for an Apple subscription - Apple Support
↳ Step 5 says to contact Apple if the prior steps didn’t bring a solution. They can assist.