Tires are tires. I had two patches, not plugs, as plugs are not safe, on my Y before I got new tires. The only difference is that on the Y, they have foam liners in the 19" wheels. Any competent tire shop simply cuts and removes it for the repair, two minutes top. They ask if you want it back in, no charge. When I got new tires, I had them remove it. I can't tell any difference.
Tesla service isn't the best place for tires. Discount Tire or your local tire shop is better. Imagine how you would hate if you had to use the local Ford/Chevrolet/ Toyota shop for tire repair. These places are geared for vehicle repairs. Tires are a side deal. Yeah, they have the equipment, not the inventory. Tire places do that.
Tesla Y doesn't come with a spare. I carry a repair kit and a compressor for emergency purposes.