This is a fascinating question to me, an admitted airline dork.
Level isn't technically an operating airline—they're more like a marketing company that uses another company to deliver tier services . That other company being their corporate sibling, Iberia. So on any Level booking, you'll see "Operated by Iberia". Even though the planes say Level, it's corporately registered to Iberia, and the crew is all certified under Iberia.
Level certainly has it's own contract of carriage, fare rules, refund policies, change fees, and such—those should all be easy enough to find. So the question becomes does Level have its own interline agreements, or does it use Iberia's? (Interline agreements are what allows say, Delta to put you on a United flight in case of cancelation. Many low-cost carriers don't have any/many agreements with other carriers.)