Switching dimmer switch with 2 black wires to regular switch

Question

I just wanted to confirm before wiring this up. When I took this off I see that two black wires going to the dimmer switch when it is normally black, white, and ground. Not sure how you tell which is exactly the neutral I need to be plugging into both screws on the new switch. I found the picture below which looks like the situation I am in currently:

Not really sure how I can tell which one is supposed to be to the load and which one is to the service panel but I want to assume that the single line that is going into the dimmer would be where I would connect the hot wire and the wing nut that has multiple wires going into it to power both of the other lights would be going to the load but just wanted to confirm based on my current setup which is this (the black wire that broke off that is in the top right went to the wing nut at the bottom just for clarification):

Answer 1

two black wires going to the dimmer switch when it is normally black, white, and ground.

There's your trouble. You're used to hooking black, white, ground to loads and sockets. You're thinking "a switch must be exactly the same as that other stuff".

Nope, a switch is not a load, it interrupts power to the load.

Since current flows in loops, interrupting the hot side is enough, so it only connects to two hot wires and does not need to talk to neutral at all.

If you have seen switches wired black-white-bare in the past, those are pre-2011 switch loops which were not properly marked - the white wire should have been re-identified with black paint or tape to indicate it is actually always-hot.

Post 2011, actual neutral must be brought down to switches, because smart switches need it.

Not really sure how I can tell which one is supposed to be to the load and which one is to the service panel

A plain switch does not care, and you don't need to either.

But if you did care, the supply hot generally serves more than one load, and the switched-hot generally serves just the light, so typically has a lonely hot wire. Typically.

Answer 2

Using a voltmeter/multimeter on an apppropriate AC voltage range (typically 200V for most multimeters and US wiring) or a non-contact voltage tester, determine (carefully) which wires are live with the breaker on and the switch turned off. Then go turn the breaker off again.

Those are the ones connected to the supply/line/circuit breaker, and it's very common for multiple wires to be joined to feed unswitched hot on to other devices on the same circuit.

None of those are wing-nuts, they are just standard wirenuts/Marrettes.

That's a Wing-Nut® (for joining wires.) It has wings, to make tightening it properly easier. Your wire nuts are not tightened properly. You don't have to replace with this sort, but you do need to tighten the ones you have properly when reassembling this mess. Several of your ground wires are not in a wirenut at all, they are just loosely twisted together. That Will Not Do.

You can either learn to connect wirenuts properly, or you can change to something easier like Wago Lever-Locks® or Ideal's push-in connectors. Beware unlisted import knockoffs of those.