Also, I’m not certain they’re flies, but they all look the same and are about the right size, and I don’t know what else they could be

When a spider is done with it's food quite often all that is left is a crumpled up ball of chitin, so you usually can't tell afterwards.

Anyhoo, I’m debating what I should do about the spider, if anything. One is fine, but I do not want hundreds more.

I occasionally have egg sacs hatching in my flat and it's not a problem. Most spiders commonly found indoors only produce egg sacs with few dozen eggs. They will usually disperse within a day or two. Maybe crack a window to allow more of them outside ... but most will just die and mix into your regular household dust.