My father has a Denali. I don’t know what year it is but I can tell you that when he drives it and when the truck warmed up for about twenty minutes of highway driving, the truck backfires then acts like it is running out of gas. What could this be? Fuel injector problems or something else?
Possible EGR system not functioning properly
Vacuum leak
Sticking valves
Could also be fuel injector problems.
If the injector(s) is(are) leaking fuel into the cylinder(s) when it(they) should be closed, unburned fuel may be making its way into the hot cat converter. That “backfire” may be explosions in the converter. The stumbling could be a bit of flooding, output from the injector(s) that’s more liquid than vapor.
The fuel pressure regulator would be another good possibility to consider.