Earth's heat is in an equilibrium with the Sun and Space. If you add a heat generator, you will see that more heat is emitted out into space and the temperature does not increase much (and stays constant after a short increase). But if you change the equilibrium point (like by adding greenhouse gases), you'll see the temperature changing quite quickly.

How do the greenhouse gases change the equilibrium point while other mechanisms of increasing heat don't?

Greenhouse gases don't simply increase heat. They change the composition of the atmosphere. It's similar to the way adding salt or alcohol to water will change the freezing temperature of the water.

Greenhouse gases don't add heat, they reduce the amount radiated to space, thus making the planet warmer.

Technically both change the equilibrium point. But one acts by adding heat, and the other by directly influencing the equilibrium.

Yes, but it's an extremely low amount compared to the heat we trap by emitting greenhouse gases.

Solar panels also add heat to the Earth, since they are black and absorb more solar radiation than a lighter-colored surface. This is also extremely minor compared to fossil emissions.