How do you store the cookies when including jam?

Nancy's advice would be applicable if the jam was used a filling like a macaron which these are not. The jam is swirled into the batter then baked so it should be pretty hard when done.

You can't swirl in the jam after the meringue is baked, the jam would just lay on top which is why it's swirled into the batter before baking.

I would likely store these in a cool, dry place in an airtight container (maybe with a desiccant pack like silica gel). I would expect the product quality to show some noticeable decline after a week or so but not any spoilage.

StephBeaty -

From experience and online baking sites, dry meringues (not sitting on a custard pie or with a wet topping) can be stored at room temperature in an air tight container for a couple weeks.

Meringues that sit atop a wet pie or have a wet topping on them, need chilled storage - a few days in the fridge, longer in the freezer.

For these cookies, consider that option. Or - modification - bake them without the jam, store dry at room temp and then add the jam just before serving.

Hope this helps.

https://www.kingarthurbaking.com/blog/2023/08/03/how-to-store-meringues#:~:text=A%20few%20tips%20for%20success,they%20can%20crisp%20up%20further.