In regards to 529, is the state "that sponsors this qualified tuition plan" the state of the recipient or the state of the payer/ owner of the 529 plan?

None of the above.

The state that sponsors this qualified tuition plan is not the state the owner or the beneficiary, of the plan,  lives in (or the "recipient", who can be either the owner or the beneficiary) .  It is not even the state in the "PAYER’S/TRUSTEE’S name, street address, city or town, state or province, country, ZIP or foreign postal code, and telephone no"  Box on the 1099-Q. 

It's the state that sponsor's (established) the plan. If you don't know which state that is, you'll need to ask the plan administrator. 

That information is not needed for the federal return, but may be for the state tax return. 

You can also look up the state here: www.savingforcollege.com.   What @Hal_Al explains above is accurate - the plan may not be associated at all with the state where the beneficiary or the payer lives - although payers often do buy the plan in their own state of residence for potential tax benefits, the only way to know for sure is to contact the plan administrator or look up the information about the plan.