Ordered and installed the Amazon Basenor mud flaps - best mod i have done yet. Ordered Tuesday, received Saturday. They we very easy to install, match perfect, and give a "factory finish" appearance to the car. They do not stick out beyond the side tire profile, in fact they match exactly. It's obvious that these were designed specific for the Model 3, and not a generic product - link below.
https://www.amazon.com/Tesla-Model-Flaps-Splash-Guards/dp/B07V36S77Y
As mentioned earlier, the front flaps require creating a hole in the plastic fender well material. Once mounted, I simply used an ice pick, centered in the flap hole, and pushed it through the fender well material. This creates a small pilot hole for the supplied mount screw to bite, and thread in. There is nothing directly behind the material, at least for several inches. Screw in snug, but no so tight as to strip out the fender well material (~1/16" rubber/plastic thickness). The rear flaps require removing and reinstalling the lower mount bolt, which is 10mm.
The wheels do not need to be removed, but turn the front wheels for better access. The supplied mounting expansion tabs are a two part composite. While the outer expansion tab inserts easy enough, the separate center plastic "spline nail" piece require a significant amount of force to insert, and access is limited. I used a 1"x1" wood board, about 2' long to seat one end on the center piece, and struck the board with a hammer while holding the outer end by hand. Basically, used the board as a striking lever for access between the tire and fender well.
Highly recommend this addition, don't know why they were not included with the car, or at least as an add-on option.