No free subscription with MacBook Air m3 purchase?

Check with the exact subscription you are looking for. For example the the 3 months free Apple TV subscription with device purchase contains this note:

This offer is not available if you or your Family have previously accepted an Apple TV+ three months free or one year free offer.

Apple TV+ - Apple

That is standard with most of the free trial subscriptions. I have seen some promos that specifically allow an additional trial period, but those are not very common and mostly were provided by carriers that wanted to provide the service with your cell plan.

You can not get more than one free trial to any given Apple service regardless of how may Apple devices you buy.

One free trial per service per Apple ID.

Then what IS the question?

If you had a free trial for Apple Music, for example, when you purchased an iPhone, you do not get another one if you purchase a Mac.

Did you purchase directly from an Apple Store, or via the Apple online store?