You might be able to DIY, depending on some extra preparation.
What's hard to see in the photos is maybe a metal 2-gang box (?) that has been stuffed full of fiberglass.
The first step is to turn off the circuit breaker(s) for both switches. Then verify there is no voltage on any of the terminal screws. I prefer a multi-tester when checking for voltage. If the paint is interfering with the multi-tester probes then leave the switch in the on position so you can verify the lights and circuits are off.
The second step is to remove all of the insulation. It doesn't belong there and could interfere with the heat sink on the new dimmer. I suggest wearing gloves for this task.
If you don't find a 2-gang box, or if you find a plastic box with no copper ground wires, then STOP.
Now the difference between the old switch and the new switch is that this new model has polarized terminals, which is why one screw is red. Due to the amount of paint on the old switch, you will likely need to remove the two black wires for testing. With those wires separated and capped or otherwise safely away from other people and metal parts, turn on the circuit breaker, then use a multi-tester to determine which black wire has the line voltage (hot). Label the hot wire, then turn off the circuit breaker.
The hot wire will attach to the black terminal. The other black wire is the light and will attach to the red terminal. Remember, no paint is allowed on the stripped wires. Clean it by scraping gently, or cut and re-strip.
"Switch on the left doesn’t do anything" is not a good reason to cap wires. It could be set up for an old ceiling fan or a wall receptacle. It's also possible the backstab connection has failed and the switch simply isn't working anymore.
Based on the comments, there is a substantial fire hazard in the existing work. Foam insulation is a flammable material and should not be present inside a junction box. The failed backstab connections are likely to arc, providing an ignition source to that insulation. Removing the broken switch and the foam should be a higher priority than the dimmer upgrade.