I have an existing concrete patio that is less than 6 months old. In my opinion, it is of high quality. It is 4-6 in thick and rebar reinforced. It is approximately 30 x 15 ft.

We are considering putting in a pool. The pool decking (concrete) will need to be tied into the existing concrete patio. Each pool vendor has a different opinion on the matter. ALL will use an expansion joint. Some want to just pour the new concrete w/o physically tying in. Others want to physically tie the two together w/ rebar, while one vendor wants to pour a rebar reinforced footer below the existing patio which would allow the existing patio to float on the new patio.

These are pool vendors and not concrete experts. What do you recommend?

Joining the 2 slabs together w/ rebar will work well. I do it quite often. Make sure all grade & gravel is well compacted. Joining the 2 will make one big slab that will float together. Make sure control joints are added in the new slab also to prevent unwanted "spider web" cracking.
Drill into the edge of the existing slab every 24" (max) and insert rebar that will stick into the new pour.

The last one you mentioned, if I understand correctly. The guy wants to install a footer under the existing patio edge and extend it under the new patio edge so the 2 slabs are supported by that footer at that joint?
If the type of soils in your area are bad this approach may be what you need. If not stick with joining the 2 w/ rebar.