Exactly.Load index is key to answering the question.
Not sure if this chart is up-to-date, but this may be a good starting point:
https://www.tsxclub.com/attachments/discount-tire-inflation-1-pdf.47187/
There are load index charts where you can find the original tire's load index and inflation value and look at what load the tire is rated to carry at the intersection of the two values and then find the closest pressure for the non-standard sized tire.
The PDF has an explanation of how to do it.
In your case, the original size seems to come in either 94 or 98 load range. I don't know which is specified for your vehicle. For this example, I'll assume 94. If 98, adjust accordingly.
From the chart, a load range 94 tire at 30psi supports 1270 pounds.
The replacement tire also comes in either 94 or 98 load range, meaning it will support just as much.
Bonus! If your tires match the load range called for by GM, then you can STILL use the pressure on the placard.
But for this example, let's assume that the new tire is a 98 load range tire. In that case, you would go to 27 PSI if I correctly understand as that would support a load of 1296 pounds.