Trade-In restricted to certain products?

This is a user-to-user forum. You are not speaking to Apple here.

Looking at Apple Trade In - Apple, I see nothing about the new device having to be a MacBook Pro. Do you have any link to information from Apple themselves saying that there is such a restriction?

There is also this.

"What if I’m not ready to buy something? 

No problem. We can put the value of your current device on a gift card that you can use anytime. Get an estimate through the trade-in tool and choose the Apple Gift Card option."

So you could presumably trade in the old MacBook Air, get the gift card, put the gift card balance into your Apple Account, and use it towards the purchase of a new MacBook Air.

But I'm guessing you were misinformed and you can do the trade-in more directly. You may want check with Apple themselves as to what the deal is, e.g., by clicking on the "Need shopping help? / Ask a Specialist" link on this page:

Apple Store Online - Apple

As far as paying down what you owe on the Apple Card, my understanding is that "Apple Card is issued and Savings accounts are provided by Goldman Sachs Bank USA, Salt Lake City Branch, Member FDIC." (Reference: footnote #1 on the https://learn.applecard.apple/apply page). I would guess that they only want money – not Apple Gift Cards or Apple Account balances.

Like Apple Gift Cards, credits from Apple trade-ins all end up being spent at Apple, not elsewhere.

If you want to buy a MacBook Air, get the gift card, and then use the gift card to buy the MacBook Air.

I’ve usually had the trade-in product review done at an Apple Store, as that avoids some questions.

Apple Gift Cards cannot be used for Apple Card payments, or for purchasing another gift card.

As for an obvious alternative to the Apple trade-in program that can provide cash, sell your MacBook Air privately.