Does the clean energy charging option recognize that I have solar panels and a back up battery when it’s extrapolating its data? Or does it go off of public energy information from local power suppliers?

... But as I live in Salt Lake City which doesn’t have very much renewable energy in circulation, I would assume in that case that it would be optimal to charge it at night when energy demand is lower.

Nothing like it. As Use Clean Energy Charging on your iPhone - Apple Support explains,

"... your iPhone gets a forecast of the carbon emissions in your local energy grid and uses it to charge your iPhone during times of cleaner energy production."

In other words your iPhone has no way to determine where it's getting its power.

To answer your question, charge it during the day, ideally when the sun is directly overhead.

That’s completely false.

when you don’t use cleaner energy like solar or wind, then there’s going to be a spike in emissions, and when renewable energy is being used, they go down.