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Build me the support chat platform that replaces LiveChat.

The difference from a simple chat box is **routing and reporting**, which is what a manager is actually buying. Build those two properly and the rest is the same widget.

STACK
- Node 20+ with Fastify, server-rendered HTML with a little vanilla JS
- SQLite through better-sqlite3, WAL mode, FTS5 over transcripts
- Server-sent events one way, POST the other
- Caddy in front

THE DATA MODEL
- conversations: id, visitor_hash, queue_id, page, started_at, first_response_at, resolved_at, agent_id, status, rating, rating_note
- messages, agents, canned as usual
- queues: id, name, skills_json, max_concurrent_per_agent, hours_json
- assignments: id, conversation_id, agent_id, at, reason — **append-only, so 'why did this sit unanswered' is answerable**
- shifts: id, agent_id, from_utc, to_utc
- escalations: id, conversation_id, to_ticket_id, at

ROUTING, WHICH IS THE PRODUCT
- A conversation enters a queue based on the page or an answered question
- Assign to the available agent with the fewest open conversations, respecting a per-agent concurrency cap. **The cap is what stops one agent holding nine chats badly**
- Skills per queue, so a billing question does not land with somebody who cannot answer it
- Reassign automatically if unanswered past a threshold, and record why
- Outside hours the queue takes an email instead and says so

THE FALLBACK, WHICH MATTERS MORE THAN THE CHAT
- Not everything is resolved in a conversation. One button turns it into a ticket carrying the whole transcript, and the visitor gets an email with the reference
- **A chat that ends with 'someone will get back to you' and no ticket is a promise nobody can keep.** Make the escalation structural rather than verbal

MEASUREMENT A MANAGER CAN STAFF FROM
- First response time and resolution time, as medians and 90th percentiles, by hour of day and day of week. Averages hide the bad afternoons
- Missed conversations: started, never answered. This is the number that justifies a hire and the one most dashboards omit
- Rating with an optional comment, asked once at the end, never mid-conversation
- Concurrency per agent over time, so 'we are fine' can be checked

THE AGENT VIEW
- Keyboard-first, unread first, canned replies by shortcut, visitor history and current page beside the conversation
- A visible personal load, so an agent can see when they are over capacity

PRIVACY
- Hashed visitor identity, transcripts on a stated retention with a sweeper, no capture of unsent typing, and deletion on request

WHAT MATTERS MOST
The concurrency cap and the missed-conversation count. One protects quality; the other tells you the truth about your coverage.