fix: Remove all non determinism

[vezenovm]

Description

Problem*

Resolves #2036

Summary*

The parent branch added a check for non-determinism in the compiler. This PR contains all fixes to get our tests passing that check. I separated them out from the check itself for ease of reviewing. This PR will go into #6847 once it is ready.

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 Brillig bytecode sizes

Generated at commit: 42af0982cd37a76bb4102a7928094b8b7e837ae4, compared to commit: cc7009fc6604a57f4aab2b3901754d7b4db1c7fb

🧾 Summary (10% most significant diffs)

Program	Brillig opcodes (+/-)	%
poseidonsponge_x5_254	+3 ❌	+0.07%
sha256_regression	+3 ❌	+0.04%

---

Full diff report 👇

Program	Brillig opcodes (+/-)	%
poseidonsponge_x5_254	4,254 (+3)	+0.07%
sha256_regression	6,920 (+3)	+0.04%

[github-actions]

Changes to number of Brillig opcodes executed

Generated at commit: 42af0982cd37a76bb4102a7928094b8b7e837ae4, compared to commit: cc7009fc6604a57f4aab2b3901754d7b4db1c7fb

🧾 Summary (10% most significant diffs)

Program	Brillig opcodes (+/-)	%
sha256_regression	+3 ❌	+0.00%

---

Full diff report 👇

Program	Brillig opcodes (+/-)	%
sha256_regression	118,707 (+3)	+0.00%

[github-actions]

Peak Memory Sample

Program	Peak Memory
keccak256	78.15M
workspace	122.63M
regression_4709	423.26M
ram_blowup_regression	1.58G
private-kernel-tail	206.67M
private-kernel-reset	720.25M
private-kernel-inner	291.85M
parity-root	171.68M

[github-actions]

Compilation Sample

Program	Compilation Time	%
sha256_regression	0m1.353s	-3%
regression_4709	0m0.796s	-4%
ram_blowup_regression	0m14.284s	-1%
rollup-base-public	3m31.506s	3%
rollup-base-private	2m58.734s	-2%
private-kernel-tail	0m1.197s	3%
private-kernel-reset	0m7.838s	-13%
private-kernel-inner	0m2.353s	-1%
parity-root	0m1.167s	34%
noir-contracts	2m37.886s	-12%