feat(email): LLM-assisted triage classification when heuristic confidence is low

[kovtcharov-amd]

The heuristic classifier caps at ~70% accuracy. Messages where `confident=False` are currently classified as `informational` — this is wrong. The LLM should classify these messages directly rather than guessing.

Tasks

• Wire LLM classification into `triage_inbox_impl` — when `confident=False`, send email body to LLM with classification prompt
• Add structured triage prompt template: `{category, confidence, reasoning}` JSON output
• If LLM classification fails, raise an actionable error (do not silently default to `informational`)
• Benchmark heuristic-only vs heuristic+LLM on test corpus
• Update integration test `xfail` to `pass` (`test_heuristic_triage_meets_baseline_minus_tolerance`)

Key files: `src/gaia/agents/email/tools/triage_heuristics.py`, `src/gaia/agents/email/tools/read_tools.py`

[github-actions]

Solid scoping — the fall-through at triage_heuristics.py:258-263 is the exact gap (currently it returns category=informational, confident=False for the no-match case and nothing escalates today). A few notes from poking at the code so this can land cleanly:

Existing hooks worth reusing

• triage_inbox_impl already records confident: bool and rationale: str on every decision (src/gaia/agents/email/tools/read_tools.py:286-307). The LLM step slots in right after _apply_session_preferences — replace the confident=False decisions in-place and update rationale so the audit trail shows "heuristic → LLM: <reasoning>".
• IMPORTANT/STARRED (rule 7) currently also returns confident=False and falls back to actionable. That's a separate "needs LLM" path — worth making sure the new classifier handles both fall-through sources, not just rule 8.
• The category vocabulary is fixed by ALL_CATEGORIES in triage_heuristics.py:70-75. The structured prompt should enforce that set or the eval scorecard in tests/integration/test_email_agent_triage.py will mismatch.

Coordination with #1066

#1066 already proposes a force_llm config flag on EmailAgentConfig that demotes every heuristic decision to confident=False. If that lands first, this issue is "implement the path force_llm already exercises." Worth deciding which PR introduces the LLM-classify code path so they don't conflict — easiest is probably: #1066 adds the flag + a stub call site, this issue fills in the real LLM classifier behind it.

Fail-loudly per CLAUDE.md

Agreed on the "raise actionable error, do not default to informational" task — that aligns with the no-silent-fallbacks rule. The error should name the message ID and the LLM error so the user can re-run on a smaller batch.

Eval gate

test_heuristic_triage_meets_baseline_minus_tolerance is currently a soft xfail (tests/integration/test_email_agent_triage.py:110-115). Flipping it to a hard pass means the baseline floor in baseline_accuracy.json becomes the regression contract — worth confirming with @kovtcharov-amd whether to also regenerate the baseline once heuristic+LLM is wired, so the floor reflects the new path's accuracy rather than the heuristic-only number.

Happy to pick this up after #1066 merges if no one else is on it.

[itomek]

Rescope: force_llm already routes low-confidence messages to the LLM (merged via #1067) — this is finish + benchmark to the >85% gate, not build-from-scratch. Gate on the signed-off action-item schema from the REST contract issue.

[itomek]

Tracking as the low-confidence LLM-assist slice of the 4-way categorization capability (#1266).