For a propane forge you *NEED* the ceramic sheath thermocouples if you want them to last more than a few sessions, especially at the upper limit of the probe temp range.
The Auberin's high temp K type thermocouples have a little bit of extra-leeway outside of the spec, and I've regularly had some of mine up at 2450+ for extended periods of time. It's not optimal, as mentioned, there are other types that are superior for temps above 2375ish.
To be clear, you not only want the K type thermocouples from Auberins that have sectional ceramic links around the wires themselves, but the test-tube shaped "sheath" they sell, that the whole probe slides down into.
You can permanently mount (mortar) the ceramic sheath into the forge, and simply slide the thermocouple itself in and out as needed. Although typically, it's best not to monkey with them. The ceramic sheath itself isn't super fragile, but it's not super durable either. I've broken a bunch of them smacking them with billets, etc.
Also, their "Universal Thermometer" works great for this application, to read the temp. You can set an alarm band, i.e. start beeping once you hit a certain temp, and stop once you go below a certain temp, or the opposite, depending on your needs. I wouldn't bother with the PID, unless you're trying to setup some automated temperature controlled forge, which IMO, is very complicated, and never very elegant, with propane forges, which one of the major advantages is typically, atmospheric control, but is difficult to maintain when you've got constantly fluctuating air/fuel ratios when using solenoids to regulate temp. Unless you're building a setup like this, the PID serves you no purpose, and is more complicated to use, and needs to be housed preferably in a project box.
A good needle valve for your fuel, and large sliding gate valve for a HIGH pressure blower (the only easily available ones on the market for us are the "Forge Blowers" that Kayne & Son's (Blacksmith's Depot) sells, and are an excellent value, and the only thing I'd recommend for a blown burner forge of any type), will let you nail just about any temp and hold it, once you understand how to tweak it, and your forge equalizes, that your burner design will allow.
If you follow this link, you can get the pyrometer, thermocouple, and sheath, all in the same page for $90, make sure to check the box for the sheath below the listing:
https://www.auberinc.com/index.php?main_page=product_info&cPath=17&products_id=282
Yes there are plenty of other options to geek out on, given time, and a thorough understanding of your needs and logistical caveats, but you can feel secure just buying the above for now, and know you didn't waste your money.. Can you find potentially the same/similar components, for cheaper? Yes, but Auberin's stands by their stuff, tons of us in the community pay a few extra bucks for the piece of mind that they're not selling junk, and will fix it if there's a problem.