If you aren't using looking to do professional recordings with them, there are very cheap 4, 6, 8, up to 10 channel mixers readily available. They aren't rack mountable but they are under a foot side so they are very small. I daily drive a four channel one and it works fine.

https://www.amazon.com/COKYISS-10-Channel-Sub … /dp/B0D6367BYV/

13 sound sources is a lot, especially if they are all stereo (26 channels total).

Something like a Behringer RX1602 or an ART MX822 are 1U rack mixers that can handle up to 8 stereo devices. If you wanted to hook up more, you'd need at least one additional mixer for sub-mixing. You could also use a patch bay, though that would involve some manual cable switching depending on how you set it up.

That "Cokyiss" mixer is exactly what I was looking for. I don't know how I missed it searching amazon and google, but that should do it.
I even like the jack placement much more than my Hart mixer

look for a Rolls RM203X, 10 stereo line ins, 1u rack.