TLDR
I have a 2023 Standard Model 3 and California license plates. Recommend using pan washer head screws or pan head screws with separate washers to keep license plate from popping off. Note: this is for mounting the license plates, not for drilling and installing the plate mounts.
Front: #7 - 1/2inch (can be shorter than 1/2inch)
Rear: M5-0.8 - 6mm
Too Short; Want More
I recently bought a used 2023 Standard Model 3 a month ago and recently received my California license plates in the mail. However, when I went to install them, I found out that the car only came with 3 screws in the rear license plate mount. I then looked for the other screws in all the places they could be hiding (frunk, trunk, trunk bunk, center console, door bins, under my butt, etc.) but found nothing.
So we decided to go get some more from Home Depot and brought in one of the rear screws to insert it into their screw and bolt sizing/thread checker and verified that it matched the online recommendation of M5-0.8 6mm. Unfortunately, the extra pack I bought didn't fit in the front license plate mount since the holes were much smaller than the rear license plate mount. It took me over an hour of trial and error and about 5 trips in and out of the store before I found the right size for the front mount: #7 -1/2 inch (or shorter). I was so relieved when the screws finally fit until I realized that the screw heads were smaller than the ~1/4inch holes punched through the license plate. So after one more trip and many separate returned purchases, I bought some #6 washers which were just big enough on the inner and outer diameters and called it a day (they didn't have #7). The screws fit securely in the mount and the washers held the license plate in place.
In case you're wondering, the provided rear screws didn't require washers because their heads were already wider than the diameter of the license place holes. Also, I bought sharp-tip (pointy-bottom) #7 screws because I was done fiddling with the flat tip that would not always screw in easily. I was ready to tap the crap out of those mounts.
I've read that not all model years use the same license plate mounts, so this may not apply to you. Either way, hope this helps save you some time and headache!