feat: use more efficient field merger code

[TomAFrench]

Description

Problem*

Resolves

Summary*

This PR replaces the value merger code reverted in #6673 but solely for fields.

Additional Context

Documentation*

Check one:

• No documentation needed.
• Documentation included in this PR.
• [For Experimental Features] Documentation to be submitted in a separate PR.

PR Checklist*

• I have tested the changes locally.
• I have formatted the changes with Prettier and/or cargo fmt on default settings.

[github-actions]

Changes to number of Brillig opcodes executed

Generated at commit: 271db0be75720d5420670adc0afc64968aa65f13, compared to commit: f065c6682e2c896a346716cf88ac285f1d4bf846

🧾 Summary (10% most significant diffs)

Program	Brillig opcodes (+/-)	%
poseidonsponge_x5_254	-3 ✅	-0.00%

---

Full diff report 👇

Program	Brillig opcodes (+/-)	%
poseidonsponge_x5_254	183,750 (-3)	-0.00%

[github-actions]

Changes to circuit sizes

Generated at commit: 271db0be75720d5420670adc0afc64968aa65f13, compared to commit: f065c6682e2c896a346716cf88ac285f1d4bf846

🧾 Summary (10% most significant diffs)

Program	ACIR opcodes (+/-)	%	Circuit size (+/-)	%
array_sort	+2 ❌	+3.77%	+4 ❌	+3.13%
regression_5252	-18 ✅	-0.05%	-276 ✅	-0.62%

---

Full diff report 👇

Program	ACIR opcodes (+/-)	%	Circuit size (+/-)	%
array_sort	55 (+2)	+3.77%	132 (+4)	+3.13%
hashmap	49,398 (+149)	+0.30%	113,174 (+161)	+0.14%
u128	641 (+4)	+0.63%	4,635 (+5)	+0.11%
binary_operator_overloading	284 (+2)	+0.71%	4,465 (+2)	+0.04%
regression_capacity_tracker	117 (+1)	+0.86%	3,972 (+1)	+0.03%
bench_eddsa_poseidon	16,441 (+2)	+0.01%	19,588 (+2)	+0.01%
references	7 (-1)	-12.50%	23 (0)	0.00%
slices	771 (+1)	+0.13%	3,893 (-5)	-0.13%
slice_dynamic_index	1,061 (-14)	-1.30%	6,473 (-32)	-0.49%
regression_5252	32,898 (-18)	-0.05%	44,246 (-276)	-0.62%

[github-actions]

Peak Memory Sample

Program	Peak Memory	%
keccak256	78.71M	0%
workspace	121.94M	-1%
regression_4709	286.66M	0%
ram_blowup_regression	1.62G	0%
private-kernel-tail	209.11M	0%
private-kernel-reset	863.60M	1%
private-kernel-inner	304.32M	0%
parity-root	174.64M	0%

[github-actions]

Compilation Sample

Program	Compilation Time	%
sha256_regression	0m1.392s	-6%
regression_4709	0m0.733s	-8%
ram_blowup_regression	0m15.995s	-3%
rollup-base-public	7m19.300s	49%
rollup-base-private	3m44.355s	14%
private-kernel-tail	0m1.440s	2%
private-kernel-reset	0m14.725s	65%
private-kernel-inner	0m2.602s	2%
parity-root	0m0.970s	-2%
noir-contracts	2m52.775s	0%