chore: PairingProverExt is vacuous

[jonathanpwang]

PairingProverExt is backend agnostic because it is vacuous and the pairing extension only consists of phantom sub-executors.

Also changed a trait bound from PrimeField32 to just Field

[github-actions]

group	app.proof_time_ms	app.cycles	app.cells_used	leaf.proof_time_ms	leaf.cycles	leaf.cells_used
verify_fibair	(-60 [-5.3%]) 1,074	322,700	17,672,408	-	-	-
fibonacci	(-29 [-1.3%]) 2,219	3,000,556	51,508,517	-	-	-
regex	(+32 [+0.4%]) 7,523	8,330,866	165,431,684	-	-	-
ecrecover	(-16 [-1.4%]) 1,145	274,568	8,596,011	-	-	-
pairing	(-51 [-1.4%]) 3,647	3,725,930	93,105,233	-	-	-

Commit: f413849

Benchmark Workflow

[codspeed-hq]

CodSpeed WallTime Performance Report

Merging #1907 will not alter performance

_{Comparing chore/pairing-general (f413849) with feat/new-execution (a62e015)}

⚠️ 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

✅ 24 untouched benchmarks