fix(agents): persist system prompt server-side instead of localStorage (#22857)

## Problem

The Admin → Agents → System Prompt textarea saved only to the browser's
`localStorage`. The value was never sent to the backend, never stored in
the database, and never injected into chats. Entering text, clicking
Save, and refreshing the page showed no changes — the prompt was
effectively a no-op.

## Root Cause

Three disconnected layers:
1. **Frontend** wrote to `localStorage`, never called an API.
2. **`handleCreateChat`** never read `savedSystemPrompt`.
3. **Backend** hardcoded `chatd.DefaultSystemPrompt` on every chat
creation — no field in `CreateChatRequest` accepted a custom prompt.

## Changes

### Database
- Added `GetChatSystemPrompt` / `UpsertChatSystemPrompt` queries on the
existing `site_configs` table (no migration needed).

### API
- `GET /api/experimental/chats/system-prompt` — returns the configured
prompt (any authenticated user).
- `PUT /api/experimental/chats/system-prompt` — sets the prompt
(admin-only, `rbac: deployment_config update`).
- Input validation: max 32 KiB prompt length.

### Backend
- `resolvedChatSystemPrompt(ctx)` checks for a custom prompt in the DB,
falls back to `chatd.DefaultSystemPrompt` when empty/unset.
- Logs a warning on DB errors instead of silently swallowing them.
- Replaced the hardcoded `defaultChatSystemPrompt()` call in chat
creation.

### Frontend
- Replaced `localStorage` read/write with React Query
`useQuery`/`useMutation` backed by the new endpoints.
- Fixed `useEffect` draft sync to avoid clobbering in-progress user
edits on refetch.
- Added `try/catch` error handling on save (draft stays dirty for
retry).
- Save button disabled during mutation (`isSavingSystemPrompt`).
- Query key follows kebab-case convention (`chat-system-prompt`).

### UX
- Added hint: "When empty, the built-in default prompt is used."

### Tests
- `TestChatSystemPrompt`: GET returns empty when unset, admin can set,
non-admin gets 403.
- dbauthz `TestMethodTestSuite` coverage for both new querier methods.

coderd/database/dbmetrics/querymetrics.go

@@ -1103,6 +1103,14 @@ func (m queryMetricsStore) GetChatQueuedMessages(ctx context.Context, chatID uui
 	return r0, r1
 }
 
+func (m queryMetricsStore) GetChatSystemPrompt(ctx context.Context) (string, error) {
+	start := time.Now()
+	r0, r1 := m.s.GetChatSystemPrompt(ctx)
+	m.queryLatencies.WithLabelValues("GetChatSystemPrompt").Observe(time.Since(start).Seconds())
+	m.queryCounts.WithLabelValues(httpmw.ExtractHTTPRoute(ctx), httpmw.ExtractHTTPMethod(ctx), "GetChatSystemPrompt").Inc()
+	return r0, r1
+}
+
 func (m queryMetricsStore) GetChatsByOwnerID(ctx context.Context, ownerID database.GetChatsByOwnerIDParams) ([]database.Chat, error) {
 	start := time.Now()
 	r0, r1 := m.s.GetChatsByOwnerID(ctx, ownerID)
@@ -4526,6 +4534,14 @@ func (m queryMetricsStore) UpsertChatDiffStatusReference(ctx context.Context, ar
 	return r0, r1
 }
 
+func (m queryMetricsStore) UpsertChatSystemPrompt(ctx context.Context, value string) error {
+	start := time.Now()
+	r0 := m.s.UpsertChatSystemPrompt(ctx, value)
+	m.queryLatencies.WithLabelValues("UpsertChatSystemPrompt").Observe(time.Since(start).Seconds())
+	m.queryCounts.WithLabelValues(httpmw.ExtractHTTPRoute(ctx), httpmw.ExtractHTTPMethod(ctx), "UpsertChatSystemPrompt").Inc()
+	return r0
+}
+
 func (m queryMetricsStore) UpsertConnectionLog(ctx context.Context, arg database.UpsertConnectionLogParams) (database.ConnectionLog, error) {
 	start := time.Now()
 	r0, r1 := m.s.UpsertConnectionLog(ctx, arg)