There's a K-3 III-specific screen protector on Amazon, but it currently shows a 1+ month shipping time. I'm guessing that means it's drop-shipped from China via container ship.
https://www.amazon.com/Puccy-Protector-compatible-Tempered-Protectors/dp/B08THVL7XD (despite the URL, it is NOT tempered glass)
Based on other replies in this thread and others, there are no other model-specific screen protectors currently available for purchase for the K-3 III. Hopefully that'll change soon, but I guess manufacturers weren't in a hurry to get these out.
There are cut-to-fit options out there, if you don't want to wait.
Edit: On eBay, I found "atFoliX 3x Screen Protection Film for Ricoh Pentax K-3 Mark III matt&shockproof" and ordered a set. They ship from Germany and will be here in 1-3 weeks. I'll report back when they arrive. There's a "hybrid glass" version, too, which I think may just be hard plastic.