fix(agent-org): harden recovery, task orchestration, and run finality

[ShiboSheng]

Summary

Part 1 of #272.

This is the backend half of #373, split out so the Agent Org runtime, persistence, recovery, scheduling, and task invariants can be reviewed independently from the UI.

Combined reference: #373

What changed

• Replaces best-effort watchdog heuristics with a pure Recovery Analyzer and a side-effecting Recovery Executor.
• Adds durable, fingerprinted recovery attempts with UTC 1/5/15-minute backoff.
• Makes Agent Org Wake dispatch idempotent and rechecks Run state before provider execution.
• Separates Run, Session, Task, Inbox, turn-intent, approval, and recovery-budget state.
• Enforces coordinator-owned task assignment, dynamic dependency graphs, durable TaskOutput, and transaction-local mutation outcomes.
• Adds atomic task-graph creation, plan-approval persistence, worker stop correction, restart recovery, and Run completion certificates.
• Prevents ownerless worker auto-claim, stale-owner theft, terminal Run mutation, empty provider nudges, and unsupported CLI Agent Org launches.
• Keeps the Rust implementation, Tauri commands, persistence changes, backend tests, and architecture audits together.

Issue #272 coverage

• E1: detects tasks with no recoverable eligible member and escalates typed repair reasons.
• E2: evaluates unread Inbox delivery per member; one member no longer suppresses another.
• E3: preserves and tests the conservative active-worker guard.
• E4: failed work returns to coordinator-controlled reassignment without wasteful peer auto-claim.
• E5: persists member/coordinator recovery budgets and stable reason fingerprints.
• E6/E7: cleans stale budgets, handles corrupt timestamps, filters Running runs in SQL, uses EXISTS, skips missed watchdog ticks, and removes repeated task × member scanning.
• Repairs the four Inbox-drain eligibility fixtures called out in the issue discussion.

Review boundaries

• 81 files under src-tauri/**
• 4 backend architecture-audit reports
• No frontend src/** or browser E2E files

Stacked frontend: #383

Verification

• PROTOC=/tmp/protoc-28.3/bin/protoc cargo test -p agent_core --lib agent_org — 178 passed
• PROTOC=/tmp/protoc-28.3/bin/protoc cargo test -p agent_core --lib lifecycle::tests -- --test-threads=1 — 5 passed
• PROTOC=/tmp/protoc-28.3/bin/protoc cargo check -p org2 — passed
• Husky scoped Clippy — passed for agent_core, core_types, e2e-test, org2, and session_persistence
• git diff --cached --check — passed
• Split boundary check — backend diff contains only src-tauri/** and architecture-audit files

Known target-branch baseline

Full workspace cargo clippy --all-targets -- -D warnings is currently blocked by unchanged warnings in the latest develop orgtrack-core and unrelated agent_core paths. The repository's scoped pre-commit Clippy passed for this change.