My first thought would be why didn't you ust leave the plants outside? Catnip - Nepeta cataria - is a vigorous and very hardy (zone 3) herbaceous perennial. It was not meant to be grown indoors and for a number of reasons will not thrive in indoor conditions.

One of the critical elements it will lack by being grown indoors is a natural period of dormancy. At this time of year, the plant would have died back to the ground and any possible insect issues moot.

I could not get the photo to enlarge clearly so I could not see clear signs of aphids but I could see what appear to be ladybug larvae, aka 'aphid killers', so quite possible aphids were present at some point.

Just cut the plants back and store somewhere cold but not freezing for the winter. Or heel into the ground if your soil is not frozen. The stems and leaves will grow back in the spring as they would normally do if planted outside.

I don't know what the bugs are but they aren't aphids or ladybug larvae. The shape looks more like thrips. The pale stippling would also indicate thrips. You also have powdery mildew.

Agree with GG that trying to grow this indoors is going to be a challenge.

Thanks for your comments - it's below freezing here now, and my understanding was catnip grows in 50-70F weather, so since they both were started late, I figured the only chance for them to continue to grow was inside.

I also read that the best time to cut is once they flower, but obviously that can't happen now.

Is there going to be any benefit to my cats if I cut them back and dry them out now? Or is this a loss?

As GG said, this is a hardy plant that requires a period of winter dormancy. It really needed to be planted outdoors when you first got it. You could try to keep it going for its first winter since it's a bit late to plant it out now. Have you got somewhere cool with lots of light such as an unheated porch? That might be your best bet to either cut it back to get it to go dormant or perhaps keep it limping along until you can plant it outside.

Looks like thrips and thrip frass, to me. I’m growing a pot full of catnip on our back patio. We had temperatures into the low teens earlier this season, both with and without an unsulating layer of snow. It’s still green and perky out there!