feat: add persisted whole-chat summary with background generation (#26657)

Adds a persisted whole-chat summary that backs the chat summary popover.
A new nullable `chats.summary` column is populated in the background
after a successful root-chat turn and pushed to clients via a new
`chat_summary_change` watch event (distinct from `summary_change`, which
is bound to `last_turn_summary`), so the popover reads `chat.summary`
straight off the loaded `Chat` with no extra query.

This is the data source for the popover and per-chat cost UI built in
#26649; the popover can consume `chat.summary` once this lands (the
field is nullable, so merge order does not matter).

## How it works

- **Generation** runs in the existing successful-turn finalize hook,
detached from the request so the user's turn is never blocked. A cadence
gate generates the first summary after one completed turn, then
regenerates every three turns, using the `chats.summary_generated_at`
freshness marker. Generation reads compaction-aware history, renders it
to a bounded plain-text transcript (short transcripts are skipped), and
asks for a 1-3 sentence summary via structured output. Failures never
clear an existing summary.
- **Staleness** is guarded by `history_version` (mirroring
`last_turn_summary`), so a background write racing a newer turn loses
while worker lifecycle transitions cannot reject a fresh write.
- **Model selection** uses the chat's configured model.

## Deferred to follow-ups

- **Cost accounting**: the `chat_messages.cost_source` discriminator and
summary/title usage recording were removed from this PR so summary
persistence is not blocked by hidden accounting rows advancing
`history_version`. Title usage recording stays on main's
`InsertChatMessages` path.
- **Model override**: deployment-wide summary generation model selection
is split into #26803; the base feature always uses the chat model.

## Notes

- Migration `000540` adds `chats.summary` and
`chats.summary_generated_at`, and recreates `chats_expanded` to expose
the new columns.
- Root chats only; shared viewers pick up the summary on their next
refetch (live watch events are owner-only).

Refs #26649

---------

Co-authored-by: Cursor <cursoragent@cursor.com>

coderd/database/dump.sql

@@ -2097,6 +2097,8 @@ CREATE TABLE chats (
     context_error text DEFAULT ''::text NOT NULL,
     last_reasoning_effort chat_reasoning_effort,
     compaction_requested_at timestamp with time zone,
+    summary text,
+    summary_generated_at timestamp with time zone,
     CONSTRAINT chat_acl_only_on_root_chats CHECK ((((parent_chat_id IS NULL) AND (root_chat_id IS NULL)) OR ((user_acl = '{}'::jsonb) AND (group_acl = '{}'::jsonb)))),
     CONSTRAINT chat_group_acl_not_null_jsonb CHECK (((group_acl IS NOT NULL) AND (jsonb_typeof(group_acl) = 'object'::text))),
     CONSTRAINT chat_user_acl_not_null_jsonb CHECK (((user_acl IS NOT NULL) AND (jsonb_typeof(user_acl) = 'object'::text))),
@@ -2202,6 +2204,8 @@ CREATE VIEW chats_expanded AS
     c.plan_mode,
     c.client_type,
     c.last_turn_summary,
+    c.summary,
+    c.summary_generated_at,
     c.snapshot_version,
     c.history_version,
     c.queue_version,