Apple does provide some tips to help, but resolution for the free subscription not appearing for you will have to come from your cell provider to link your Apple Account. If you started a subscription through Apple and are on the 7 day free trial, you will be billed for that service if you do not cancel.
Connect Apple subscriptions from your wireless carrier or other provider to your Apple Account - Apple Support
Have you logged into your T-Mobile account online? The instructions to activate provided by T-Mobile are:
T-Mobile postpaid wireless consumers click here to log into your T-Mobile account and add your offer. Once you add your Apple TV+ On Us feature, you will be prompted to activate your subscription with Apple. If someone other than the Primary Account Holder attempts to redeem with Apple, Apple will send the Primary Account Holder a One-Time PIN for verification. If there is no Primary Account Holder designated on the account, the oldest phone number will become the designated phone number.