I routinely check the oil level in my cars and trucks. The level read "OK" on Tuesday, but yesterday it read "Add max 2 quarts, may continue to drive". Then last night it said "OK". This morning, it again says for me to add 2 quarts.

The car was plenty hot when I checked, so the temperature shouldn't be an issue. Is it possible I have a faulty sensor, or are these motors prone to burning oil?

Never burned a drop in my two 991s.

Never put a drop in my 2014 CTTS.
My new one was delivered with the oil level close to minimum (PDI screwup)
so dealer topped it off for me.
so far no drop in level.

Are you strictly following chk oil instructions per manual?
I miss the ol dipstick

Burning through oil is normal for high HP cars. I would just top it off and see what happens. Maybe it was on the border line of being low and normal from the start.

Not 100%, but pretty certain that the new Cayenne Turbo is the same 4.8 TT with tweaks. Historically speaking, Porsche states that burning 1 quart of oil every 600 miles or so is normal in the CTT. You will find plenty of threads on it here over the years.

Depends on how you drive . Hard style with sport button on consumes a bottle of mobile 1 in 1000-3000Km . Same with both my P cars

In mostly hwy driving and a fair amount of full boost passing I used 1 litre in 4000 km in my 06 CTTS. My old 05 CTT used a litre about every 1500-2000 km. I am keeping a log so will keep checking as time goes on

So this is normal. Good thing I have a good supply of 5W-40 Mobil 1 Synthetic in the garage. Dealer added oil for me when I stopped by, but if this is a once a month event, I will just do it myself.

So I am now unable to get a reading on the oil level. When I try, it tells me that it is unavailable. I've driven a good 25 miles since they topped it up Has anyone had this issue on their CTTS?

And today, it worked. So odd.

Mine works fine

2,500 miles and no consumption on my 15 CTT. Mostly highway miles

Based on what you reported, you have erratic readings that should not be trusted.
If you simply add oil, there is potential to overfill.

I would take a picture of the display when it gives low oil indication and then also the next day when it shows/displays 'normal' level.

I would bring this info to the dealer and have them investigate a potentially malfunctioning oil sensor.

So happy my older CTTS has a dipstick...

I didn't think that any cayenne had dipsticks for the transmission??

Nope, but it has one for the engine oil. The newer Cayenne's don't.