Crankset compatibility: Specialized Stout XC vs. SRAM GX 1000 GXP

I need to replace the crankset on my Specialized Rockhopper 29 Expert (year 2017) due to damage. I would prefer not to replace the BB to minimize the cost/effort.

The original crankset is described by Specialized as:

Specialized Stout XC, 2-piece 2×10, 24mm spindle, anti-corrosion
hardware“

and the BB as

BSA threaded, external bearing, 73mm width

I have concluded that since most of the drivetrain is SRAM (except of the rear derailleur weirdly), the crankset SRAM GX 1000 GXP would be a suitable replacement since it features 24 mm spindle, has the same 36/22T, the same BCD, setup and looks generally similar on pictures (yeah, I know).

Unfortunately, it fits pretty well, except of one minor detail – the shaft seems a bit too long and there is couple mm wiggle space left when I install the left crank. I have since learned that the BSA threaded is something else than BB30 that the SRAM GX 1000 GXP apparently features, even though they have the same radius. I am very confused by all the different parameters to watch for.

What I want to ask – is there an adapter for this? Or simpler – what should I buy that will fit the BB? Or is this is a lost case and I need a new BB? I do not really feel a need to upgrade the 2×10 setup and just want to fix the bike.

Thanks for help!

Edit: I have found here that the Shimano and Sram Threaded BBs differ. Since my spindle is 24 mm all the way, it is probably compatible with the Shimano system. Would e.g. COMET MODULAR CRANKSET work on my bike better then?