feat(tools): agent-callable verify/critique tool (agent decides to spend test-time compute on self-review)

[Hmbown]

Idea

Give the agent a tool it can CHOOSE to call to run an adversarial self-review of its own recent work before claiming done — spending extra test-time compute (elevated reasoning + an independent critic) exactly when the agent judges it warranted. This is the model-decided version of the multi-lens verification that catches "green-CI-but-wrong" bugs (it just caught #4181 shipping a CLI-only fix that 16/16 CI called done).

Shape (agent DECIDES to call it)

• A new tool in crates/tui/src/tools/ (name TBD: verify/review/critique), registered in the tool catalog so the model can invoke it.
• Input: what to verify (a claim/change description + optional scope: recent diff / files / the requirement).
• Behavior: run an adversarial critic pass at HIGH/MAX reasoning (regardless of session tier) — ideally an independent critic sub-agent (reuse existing sub-agent infra) prompted to REFUTE / find correctness gaps, missed requirements, edge cases. Return structured findings (issue, severity, fix) the agent must address.
• The tool DESCRIPTION guides WHEN to call (before claiming a non-trivial change done; after a risky edit; when uncertain) — so the agent decides, not an always-on watcher.

Why

Test-time compute → better answers, spent on demand by the model's judgment. Folds in the intent of #3982 (advisor watcher) and the Advisor-role idea, but as an agent-invoked tool.

Acceptance criteria

• The model can call the tool; it runs a critic pass at elevated reasoning and returns actionable findings.
• Bounded (a verify call cannot itself recursively spawn verify); config/opt-out for cost.
• Tests: tool contract + a critic-finds-a-planted-bug test.

Target: v0.8.69 (post-stopship).

[Hmbown]

Related family — cross-link (complementary, not duplicate). This is the agent-invoked shape of verification. It differs by WHO triggers:

• feat(tools): agent-callable verify/critique tool (agent decides to spend test-time compute on self-review) #4196 (this) — the agent decides to call a critic pass.
• v0.9.4 Subagents: add an optional advisor watcher for live turns #3982 — an automatic advisor watcher on live turns (off by default, rate-limited).
• v0.9.4 WhaleFlow: verification gates (compile, test, lint, review as post-agent hooks) #4013 — deterministic post-agent hooks (compile/test/lint/review).
• v0.9.3 Engine: stream-rule injection — abort mid-token and retry with a corrective rule #3997 — mid-stream corrective rule injection.

These should share ONE critic/review engine (spawn an independent critic sub-agent at elevated reasoning). Designing #4196's tool so that engine is reusable by #3982/#4013. Also see the Advisor-role idea (selectable Fleet roster role) which would consume the same engine.