How could I use liquid flavorings to make a version of a jelly-topped cookie?
Fruit preserves have a lot going on. They have a lot of sugar and pectin and sometimes fiber from the fruit. They have already been boiled for a while and the fruit flavors that are left are there to stay.

Liquid flavorings are mostly alcohol with volatile flavoring compounds. They are added late to a recipe because they boil off easily- at a lower temperature than water boiling.

I don't know of a way to prepare liquid flavoring so that it will be less volatile. I can't think of a time that I've seen that done. Perhaps if you mixed it into another jelly that would buffer the heat during baking. Perhaps an apple jelly with your flavoring mixed in. I suspect most of the flavor would still boil out unless you added the jelly right at the end of baking.

I think you would have more success with making a topping that you can add after the cookies are baked. It would be a different texture without the candied edges but it would still be good. Pectin NH glazes are used commercially for this kind of thing.