TLDR: 2022 Model 3 with Pirelli PZero tires come with a "hidden" hazard warranty that covers punctures/impact etc through Pirelli, NOT Tesla.
I accidentally drove through one of the largest potholes I've ever seen this morning and damaged my right front and right rear tires (impact bubbles on both sides of each). Tesla advised me that they would charge me full price for new tires plus installation etc. Tesla stated they are not an "authorized" Pirelli provider (even though they are mfring cars with the tires installed) and so they would charge me. Tesla also stated that the Pirelli tires do not come with a hazard warranty, however, I found today that this is just incorrect by contacting Pirelli corporate.
Pirelli told me, and provided documentation, that explains the PZero included with the new car purchase are actually covered by a special Pirelli hazard warranty because the tires contain their "Pirelli Noise Cancelling System (PNCS), and sensorized systems" technology. They advised that, instead of going through Tesla directly, I should go to an authorized Pirelli reseller/installer and they provided a list in my area. Within 3 hours, I had 2 brand new Pirelli Pzeros installed at no cost to me. Tesla verbally quoted me upwards of $450 per tire and had provided incorrect information about the hazard warranty.
The fine print is basically that the hazard incident has to occur within the first year of ownership and the tire tread has to be above a certain threshold still. The shop measured my tread, submitted to the Pirelli rep, confirmed I was within the limits and did the replacement with no further questions asked. I'm about 1 month into ownership and have 2K miles on my car so I met all the conditions.
So, if you damage your new Pirelli Pzeros accidentally within the first year and within tread wear limit, DON'T go to Tesla. Go to an authorized Pirelli shop for warranty replacement. Contact Pirelli for the proper shop in your area. Keep in mind if they mention "Discount Tire Stores" that they will NOT honor it, but you need to go to their sister store (which is under the Discount Tire umbrella) America's Tire. Discount Tire will not honor the warranty, but their sister shops - America's Tire, will. It seems the Pirelli reps get confused by their association and recommend the incorrect locations. So if they send you to Discount Tire, question it and ask them for the nearest America's Tire instead.
I've attached a copy of the Pirelli warranty documentation and a sample of what some of the damage to my tires looks like.