If I may reply, we also spent 3 weeks on Sicily in our Cali in May 2023 - it was magnificent!
You have pretty much covered all the good spots, but whatever you do, don't miss Ragusa and Erice! Our two favourite towns in all of Sicily, and on the top 5 of all towns we visited (we drove down through Italy's west coast). Palermo can be skipped, not too impressed with that. Noto and Ragusa are similar, and as I said the latter is far superior!
There are quite a few wild camping spots perfect for Californias. The absolute top (literally) spot is at a small monastery, Santuario della Madonna dell'Aiuto, near the village Roccafiorita. It is on the top of a mountain (check the forecast for heavy winds), you have views of the Messina Strait on one side, and Mount Etna and foothills on the other! Google Maps coordinates: 37.928417330406404, 15.262501878836408. It is also on Park4Night. It is a long windy road to get up there, and feels completely isolated, even though there is the monastery and even a small restaurant nearby.
The other one is a large grassy parking lot on the north side of the island south of San Vito lo Capo. People park there during the day to get to the rocky (and beautiful) beaches, but in the early evening the crowd dissipates. We shared the space with two-three other campers, magnificent views of the ocean and surrounding hills. 38.11150984414507, 12.724362971723696.
Also, do stop at Tropea on the way down - fantastic town. Park down below and bring your walking shoes, those streets up to the center of town are STEEP!
And if time permits, you will not regret spending a few days at Cinque Terre on the way! Stay in one of the towns and take the train or boat to the others.
Have a great vacation!
And about Mount Etna - we drove up to the parking lot at Sapienza and walked around the small crater nearby, Cratèri Silvestri. We had three kids in tow, two of them eight months old, so couldn't do the summit hike/4wd

. But we got to see plenty of Etna and surrounds, and got the feel of the volcano at the Silvestri crater.