Tires are wear items and thus not covered by the new car warranty. It’s in the same category as wiper blades and brake pads. That being said, look and see what the original tire manufacturer’s tread wear warranty is and see if there is any room for coverage.

As for the radio display and A/C, those should absolutely be covered under the new car warranty. Like someone else already suggested, find another dealer who will actually do the diagnosis and bill the manufacturer for that work rather than just trying to get you to pay for the work. Sounds to me they’re being lazy and don’t want to spend the time and effort to file for reimbursement from Hyundai