Definitely not 40. More like 20, give or take.
I base tire pressures off of the stock TJ tires, which were 30X9.50R15LT B on most trims at 29 psi. This leads to 1376lbs of carrying capacity per tire, for a total of 5,500 lbs. which is a reasonable baseline for what a Wrangler at road speeds needs. TJ and YJ need the same pressure since they are the same size/weight. You can use the YJ tires as a starting point, but honestly they were way overinflated from factory. The TJ got it right.
Use this
tire pressure calculator
So, start with the "stock" tire on the left:
LT (bottom option)
30X
9.50
R15
B (96)
29 PSI
Now select the new tire:
33X
12.50
R15
C (108)
View attachment 122998
You can see the tire calculator recommends 25 PSI, because LT thigh flotation tires (inch size) are only rated to a minimum 25PSI. However, this tire at it's minimum pressure still has extra capacity over stock by 389 lbs per tire. That's an added 1,556 lbs total to the carrying capacity of the Jeep, which is excessive.
So, I would want to lower the pressure even more. How I figure out where I would want to put it, is I play with the calculator some more. I now enter the 33x12.5 info in the left side and change the PSI so I can watch how much the load carrying capacity changes with 1psi.
View attachment 122999
View attachment 123000
Changing from 35 PSI to 34 PSI, you can see the load capacity changed by 41 lbs.
This means that for every 1 PSI, the tire carrying capacity drops by 41 lbs. So take the 1765, subtract the 1376, you get that 389 lb number I referenced earlier. 389/41 = 9.48, so 9. You'd want to actually run 16 PSI to support the load like stock.
That sounds crazy low, but in reality you can try it and go from there. You can also do the chalk test, but I don't really like the chalk test. You could keep it at 20 PSI if you felt better about that. But at an absolute maximum, I would not be running them higher than 25 PSI, and that still has a much higher carrying capacity than stock.