feat: Restore VK tree

[sirasistant]

Restores verification in the VK tree. Adds support for Honk and ClientIVC verification keys in the circuits.
We still have an exception for Tube though, since it's still not a single VK.

[github-actions]

Changes to circuit sizes

Generated at commit: 0c925dcd3bdc26e0ca20890d9562c08d4312fa5a, compared to commit: 9445a4fba8e3092c3948ffe9d5eaf5f679fce89c

🧾 Summary (100% most significant diffs)

Program	ACIR opcodes (+/-)	%	Circuit size (+/-)	%
private_kernel_empty	0 ➖	0.00%	+936,476 ❌	+26863.91%
private_kernel_tail	+62 ❌	+1.33%	+524 ❌	+5.81%
private_kernel_tail_to_public	+62 ❌	+0.21%	+523 ❌	+1.32%
private_kernel_inner	+61 ❌	+0.14%	+523 ❌	+1.00%
private_kernel_reset_4_4_4_4_4_4_4_4_1	+59 ❌	+0.17%	+519 ❌	+0.70%
private_kernel_reset	+59 ❌	+0.06%	+520 ❌	+0.11%
rollup_merge	+122 ❌	+3.32%	+1,051 ❌	+0.06%
rollup_root	+120 ❌	+1.68%	+1,050 ❌	+0.06%
rollup_block_merge	+120 ❌	+1.67%	+1,048 ❌	+0.06%
rollup_block_root	+128 ❌	+3.10%	+1,513 ❌	+0.05%
parity_root	+28 ❌	+0.52%	+1,847 ❌	+0.05%
public_kernel_merge	+62 ❌	+0.12%	+520 ❌	+0.05%
public_kernel_tail	+9 ❌	+0.00%	+461 ❌	+0.02%
rollup_base	+58 ❌	+0.01%	+518 ❌	+0.02%
empty_nested	0 ➖	+∞%	-5 ✅	-23.81%
empty_nested_simulated	0 ➖	0.00%	-5 ✅	-23.81%
private_kernel_empty_simulated	0 ➖	0.00%	-5 ✅	-23.81%

---

Full diff report 👇

Program	ACIR opcodes (+/-)	%	Circuit size (+/-)	%
private_kernel_empty	671 (0)	0.00%	939,962 (+936,476)	+26863.91%
private_kernel_tail	4,710 (+62)	+1.33%	9,545 (+524)	+5.81%
private_kernel_tail_to_public	29,890 (+62)	+0.21%	40,033 (+523)	+1.32%
private_kernel_inner	44,103 (+61)	+0.14%	52,877 (+523)	+1.00%
private_kernel_reset_4_4_4_4_4_4_4_4_1	34,956 (+59)	+0.17%	74,998 (+519)	+0.70%
private_kernel_reset	91,992 (+59)	+0.06%	468,250 (+520)	+0.11%
rollup_merge	3,795 (+122)	+3.32%	1,897,297 (+1,051)	+0.06%
rollup_root	7,273 (+120)	+1.68%	1,900,452 (+1,050)	+0.06%
rollup_block_merge	7,289 (+120)	+1.67%	1,900,466 (+1,048)	+0.06%
rollup_block_root	4,252 (+128)	+3.10%	2,838,780 (+1,513)	+0.05%
parity_root	5,427 (+28)	+0.52%	3,776,972 (+1,847)	+0.05%
public_kernel_merge	53,594 (+62)	+0.12%	1,104,122 (+520)	+0.05%
public_kernel_tail	258,433 (+9)	+0.00%	2,270,721 (+461)	+0.02%
rollup_base	483,231 (+58)	+0.01%	3,356,255 (+518)	+0.02%
empty_nested	0 (0)	+∞%	16 (-5)	-23.81%
empty_nested_simulated	1 (0)	0.00%	16 (-5)	-23.81%
private_kernel_empty_simulated	1 (0)	0.00%	16 (-5)	-23.81%

[LeilaWang]

🔥

[ludamad]

🔥

Seconded :D