They'll probably be small enough to fit through the fishnet you have there, in which case they'll scatter and balloon away naturally when it's time for them to. Unless you wish to keep them all? It could be 20-50 babies if a healthy batch, and they're very difficult to feed if you want to separate them into individual containers so that they don't cannibalise their siblings. Slings are difficult, haha.
There's also a chance she's mated enough that she'll keep making egg sacs, so plenty of babies everywhere. I'd say to let them go, just because of the dedication and effort needed for spider husbandry.
But if you're up for the task, you could extract the babies when they first hatch and have had their first molt (1st instar so that they're not just eggs-with-legs). You'll start seeing the babies explore a little when that time comes, which can be a few months from now. There are a lot of resources on jumping spider husbandry available online, people who've got experience in it that I do not, so it would be best to have a read through those, to make an informed decision as well as to prepare for whichever decision you end up making about the babies.
I’ll probably release them for now. Thanks for the detailed comment.