aren’t you still limited by ambient air temp because the hot side of the Peltier needs to be cooled by air anyway?

You can certainly get subambient. Put some electrical current through a Peltier and one side gets cold, and the other side gets hot. Use the cold side to cool your components, and get the heat away from the hot side, and you can make it work.

It can be a bit tricky. The hot side is right next to the cold side and it gets really hot, so if you can't get the heat away it'll leak right back over. Peltiers use a lot of power so you need a beefy power supply, and that'll be another source of heat. Assuming you can figure that all out, you also have to be careful that the cold side doesn't get too cold or you get condensation. Electrical components tend to not like moisture very much.

I remember people experimented around with it back in early-mid 2000's. General consensus nowadays seems to be is that it's not terribly effective or practical and not worth the trouble.