chore: use explicit Result<_, ExecutionError> and pre_compute* returns StaticProgramError

[jonathanpwang]

Remove arch::execution::Result = Result<_, ExecutionError> because our use execution::* makes it a confusing arch::Result typedef.

Moreover all pre_compute functions should return StaticProgramError to distinguish from ExecutionError which is for runtime errors.

[github-actions]

group	app.proof_time_ms	app.cycles	app.cells_used	leaf.proof_time_ms	leaf.cycles	leaf.cells_used
verify_fibair	(+21 [+2.0%]) 1,060	322,675	17,672,108	-	-	-
fibonacci	2,194	3,000,556	51,508,517	-	-	-
regex	(+77 [+1.0%]) 7,564	8,330,866	165,431,684	-	-	-
ecrecover	(+17 [+1.5%]) 1,118	274,568	8,596,011	-	-	-
pairing	(+94 [+2.6%]) 3,732	3,725,930	93,105,233	-	-	-

Commit: f97261f

Benchmark Workflow

[codspeed-hq]

CodSpeed WallTime Performance Report

Merging #1898 will improve performances by 52.25%

_{Comparing INT-4466 (f97261f) with feat/new-execution (41c2b4b)}

⚠️ Unknown Walltime execution environment detected

Using the Walltime instrument on standard Hosted Runners will lead to inconsistent data.

For the most accurate results, we recommend using CodSpeed Macro Runners: bare-metal machines fine-tuned for performance measurement consistency.

Summary

⚡ 2 improvements
✅ 22 untouched benchmarks

Benchmarks breakdown

	Benchmark	BASE	HEAD	Change
⚡	benchmark_execute[keccak256_iter]	139 ms	124.8 ms	+11.37%
⚡	benchmark_execute[quicksort]	58.8 ms	38.6 ms	+52.25%