fix(ci): derive merge-group node-dep provisioning from the gate registry

[4444J99]

Problem

Follow-up to #1312. That PR fixed worker-check failing in the merge queue (empty node_modules) but provisioned only web/worker + moneta via a hardcoded path check. #1265 also touches spec/**, which implicates the web-build gate — so its merge-group integration verify then failed with ERR_MODULE_NOT_FOUND: 'yaml' from web/app/scripts/generate-static-data.mjs: web/app's node_modules was never installed. Hardcoding a third dir would just defer the next miss.

Fix

Replace the hardcoded path checks with scripts/provision-merge-group-node-deps.py, which derives the dirs to install from the SAME registry + implication logic verify.py --integration uses (load_registry / changed_set / select): for every gate the merge-group diff implicates whose command is cd <dir> && npm ..., run npm ci in <dir>.

• A new node gate is covered the moment it lands in gates.yaml — no dir list to keep in lockstep (the repo's derive-don't-pin pattern, like check-gates).
• Gates that only run a root-level node script.mjs on built-ins (contract-schemas) need no install and are correctly excluded.

Verification

• Derivation unit-checked: #1265-like diff (web/worker + spec) → ['web/app', 'web/worker']; moneta-only → ['moneta']; python/docs-only → [] (no-op).
• scripts/verify.py --changed green — incl. merge-queue-contract-test, workflow-yaml, check-gates. ruff clean.
• Touches only .github/workflows/** + scripts/** → its own merge_group implicates no node gate → merges clean.

Completes the merge-group node-dep fix so #1265 (and every future spec/web-app/worker/moneta PR) passes the queue.

🤖 Generated with Claude Code

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Review details

⚙️ Run configuration

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📥 Commits

Reviewing files that changed from the base of the PR and between 7a5101a and 312d8b0.

📒 Files selected for processing (2)

• .github/workflows/pr-gate.yml
• scripts/provision-merge-group-node-deps.py

✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Commit unit tests in branch fix/provision-node-deps-derive

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