8*6 concrete slab
I am doing something not so similar to you project but with a similar 8' by 6' space.
I am surprised that you had no replies so decided to write. Even if you have started/completed your project.
Patios are not considered part of the house/dwelling so the footer may not be required. One of my new houses in Florida, the patio just had a ~4" slab, no footer and a light weight aluminum cover with screens, did not live there long enough to see it slide from the house. I am almost sure it had an expansion joint between patio slab and house foundation.
My home in Alabama built in 1965 has a 5' wide by 30' slab on the front porch with 4 14 foot wood columns with no footings and the slab has moved away from the house 1/2 inch in the +40 years. The house has brick veneer all around and its slab is 2.5 feet below the hard clay grade. The front porch entry way described above does not look too bad.
Your BBQ slab maybe needs the footing only on the one side too keep it from moving away from the house so it will not creep 1/2" in 40 years or worse.
You mentioned rebar. For sure you will add a gravel foundation (I used 4" foundation for a paver patio 10 years ago which withstood the 5lbs hammer, 3 strikes, 12" nail penetrating test) metal screen (these are 4" by 4" or so).
I am thinking of using rebar in my 8' by 6' project. I am adding concrete over an 8' by 6' side porch portion of the main house slab (all one slab if I recall the photos from 1985) to level it with the rest of the house. The rebar should help hold the new +3" concrete slab that I'm poring over the existing patio slab. Thinking of drilling the existing slab, placing rebar 1 1/2" into the new slab. Have not seen photos of using rebar in this way, to hold a 2nd slab in place.
8' by 6' and 3" or 4" deep is 12 or 16 cuft. Have read that < 27cuft of concrete can be done by hand by one DIY.
Will send photo of my project space if someone writes back.