fix: dedupe active live conversation sessions

[shaypal5]

Summary

• Reuse an existing non-stopped live conversation session when the operator starts live mode for the same DM conversation again.
• Return normalized session payloads with existing: true|false so callers can distinguish reuse from creation.
• Update dashboard status copy and API docs to describe idempotent live-mode starts.

Validation

• npm test -- --run tests/api-auth.test.ts
• npm test
• npm run check
• git diff --check
• npm run build

Milestone

• Checked open repository milestones with gh api repos/agent-comms/agent-comms-core/milestones; none were returned.

Closes #81

[shaypal5]

Self-review after implementation, taking the requested outsider/senior-dev stance:

1. The first version only fixed sequential duplicate starts. It still allowed two concurrent POST /operator/live-conversations requests to both observe no existing session and insert duplicate non-stopped sessions for the same conversationId.

Recommended action/fix: enforce the invariant in the database, not only in application code. Add a partial unique index on live_conversation_sessions(conversation_id) where status <> 'stopped' for both D1 and Postgres migrations.

Applied: added 0007_unique_active_live_sessions.sql in both migration trees.

2. Once the database owns the invariant, the create handler must handle the natural race loser path. A request can still pass the pre-read, hit the unique constraint on insert, and should return the canonical active session instead of surfacing a generic 500.

Recommended action/fix: after insert failure, re-read the open session for the conversation. If found, return it with existing: true; otherwise rethrow the original error.

Applied: added findOpenLiveConversationSession(...) and race recovery around the insert.

3. The test coverage needed to prove more than the happy sequential path.

Recommended action/fix: keep the sequential reuse and stopped-session restart tests, and add a targeted race simulation where insert fails after another session appears.

Applied: expanded the live-session mock and added the concurrent-create race test.