If you ever have done a trial subscription to these services before, then you may not be eligible for another free trial. One offer per service per user per lifetime, afaik. See the terms and conditions:
Apple TV+ offer - Terms and conditions - Apple (US)
Apple Music offer - Terms and conditions - Apple (US)
Apple Arcade offer - Terms and conditions - Apple (US)
Apple Fitness+ offer - Terms and conditions - Apple (US)
Apple News+ offer - Terms and conditions - Apple (US)
from: Current offers - Apple (US)
(other countries and regions may have their own terms and conditions page.)
Even without the notifications, you can redeem offers in the corresponding app on the qualifying device, while you are eligible. A redeem button would appear there, based on the Apple Account and specific device. You shouldn’t try to redeem on a different device, as the special offer may not get applied there.