I can't speak to whether the quartzite is an appropriate backsplash for the Bluestar, but if you haven't installed your cabinets yet, a simple solution would be to pull them back from the wall a fraction of an inch to get to 24". Some people do that by design to have deeper counters next to the range.

You could cut the drywall.

And replace the combustible wall studs while your at it:

BACKGUARD

•  All rangetops require a backguard. Most models have the option of using: grate height trim; island trim; 6” inch standard; 17” inch hi-back; 24” inch high shelf. Heritage Classic models require a 24” inch high shelf for all installations.
•  If you are using an island trim or grate height trim, a six inch clearance between the back of the rangetop and a combustible surface is required. If an island trim is to be used without this six inch clearance, the back wall must be constructed using non-combustible and heat resistant materials that extend below the top surface of the range a minimum of six inches.
•  All backguards follow the same basic installation. Remove rear grates, slide backguard over rear of unit, align holes, use hardware supplied to fasten backguard to unit. A minimum of six sheet metal screws (more depending on width) are to be installed, three on each end and more along the bottom edge.
•  Remove the two rear ring grate/top grates from the cooktop surface. Sheet metal screws must be installed - down - into the cooktop support. Screws are installed on each end ring grate/top grate position. Replace the removed grates.
• Page 15

Just to pile on: engineered quartz counts as combustible; sheetrock counts as combustible, wood studs count as combustible, even wood picture frames on the opposite side of the wall count as combustible. "Distance to combustibles" is a dagger that penetrates in every direction specified unless an approved means of protection is utilized, such as a backguard. See IMC Section 308.

I remember trying to plan out the details around my BlueStar rangetop and wanting more precise dimensions. Just let me know what you need. If you have 23.8 inches from backsplash to cabinet face, your rangetop will be protruding quite a bit. The “seam” between the front and main part of the rangetop will be .2” past the cabinet face. If you don’t mind the “very protruding rangetop” look and have cabinet/drawer faces covering the seam, it should be fine. In my last picture I pulled my crumb drawer out to replicate how far out it would be in your case (then you have to imagine the entire rangetop pulled out to match that).

We have 1.5” extra cabinet depth here, and a large 1.75” countertop overhang. We are planning a standard/thin backsplash which will probably push our rangetop out another 1/8” or so, but I don’t want it protruding any further.

I just remembered too that there is a screw on the back of each side of the rangetop that would prevent you from pushing it all the way to the backsplash IF the backsplash goes down lower than the countertop surface. The top of the screw is 5/8 below my countertop surface, but that will also depend on how high your rangetop is sitting. My edge trim pieces are right at the minimum 11/16” height past the countertop.

Picture of the screw on the back