Nail in tire. Looking for advice

Year old CPO with plenty of tread remaining. Got a nail in the tire within a month after taking possession. Just my luck :(( Went to Costco to get it checked out and they said the nail seems fixable from the outside but I’ll need to get on schedule to determine the exact next steps incl whether I need new tires.

Costco has been amazing for me so far. Just got a set of 4 all weather tires for my commuter sedan and it runs great. But given the Cayenne is my first luxury car, idk if I should decide against going for non porsche certified stores for any work on the tire. Do people do that here? Btw while I was at Costco getting the initial assessment (where they figured out the nail as the culprit for low pressure from a cursory visual inspection) I saw a Carrera 911 gts in the shop so I have one data point haha. Looking to gather more insights coz first expensive car I’ve ever driven and I don’t want to screw it up.

I’m still under CPO warranty and have some other protection plans I bought from the dealer but I forewent the tire protection plan coz I figured by the time I’d need new tires I’d be okay paying out of pocket. But man getting this expense a month in stings lol.

So tl;dr do get tire nail in tire fixed at Costco or not? And does it impact warranty