If it’s a quality control issue then it should be covered under the Apple limited warranty; Amex extended warranty will only cover things that would have been covered under Apple’s warranty, and only after Apple’s warranty runs out.

If it’s due to physical damage or something like that, then it would fall under purchase protection. Since the issue happened within the 90 days you should be fine, it’s okay to get it repaired outside the 90 day window (just check the t&c to confirm what the deadline is for filing a claim)