Nashville and Memphis are the hot spots really with a few other Places mixed in but all in all travel inn TN is not restricted right now. Mask mandates are in force but that is only prudent. There is no real "off" season in the Pigeon Forge/Gatlinburg/ Sevierville area. We seem to ALWAYS be busy, just some times more than others but still busy. Campground space is usually not a huge problem because if someone is full there is another place that isn't.
If I were to recommend a time to come September would be it. Yes, last summer was a bit warm but not as hot as the year before was. Weather is up to mother natures whim. A roll of the dice so to speak as to what you will run into in either the spring OR the fall. Today, 12/10. was 62 and mostly sunny. Beautiful.
What are you looking to travel to and do? I can say that TN state parks are top notch if that is what you like. No shortage of private parks most eveywhere you go either. Choices are plentiful.