We have a '22 with the 12" screen, and I installed the 12" version of the one Briguy6 recommended, the "Spigen Tempered Glass Screen Protector [GlasTR Slim] designed for Ford F-150 Lightning (2022) / F-150(2021/2022) 12 inch Touchscreen - Matte/Anti Fingerprint" found here on
Amazon this morning. It's similar to what I have installed and run on phones for years, and I have used Spigen products in the past. There are some cheaper options, but I liked the glass/9H hardness and the matte/anti-fingerprint/reduced glare claims, along with Briguy6 and the strong reviews on Amazon (albeit for other models), so I decided to try it.
I ordered 2 in case the first install didn't go that well (let's just say I know myself too well...) and am glad I did. I accidentally put a little pressure on the first one I opened just trying to get situated in the car and cracked one corner of it. Thankfully I was able to get a good install on the second though. The white speck in the lower left corner of the photos below was on top and brushed off. I can take some with the screen on if anyone wants to see that. I haven't had it in all sun/glare conditions yet, but so far I think it looks pretty good.
Hardest part of the install is getting it lined up. They have come out with some pretty great options for assisting in lining up phones these days, but on these you have to just take your time, eyeball it, and wing it. I will say while I normally follow the directions and use the alcohol wipes, microfiber cloth, and dust removal stickers provided, I didn't here. We just took delivery last Friday and I left the protective plastic on the screen until just before install. I pulled it off and figured it wasn't getting any cleaner and immediately installed the protector.