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.

codersdk/chats.go

@@ -202,6 +202,16 @@ type ChatModelsResponse struct {
 	Providers []ChatModelProvider `json:"providers"`
 }
 
+// ChatSystemPromptResponse is the response for getting the chat system prompt.
+type ChatSystemPromptResponse struct {
+	SystemPrompt string `json:"system_prompt"`
+}
+
+// UpdateChatSystemPromptRequest is the request to update the chat system prompt.
+type UpdateChatSystemPromptRequest struct {
+	SystemPrompt string `json:"system_prompt"`
+}
+
 // ChatProviderConfigSource describes how a provider entry is sourced.
 type ChatProviderConfigSource string
 
@@ -681,6 +691,33 @@ func (c *Client) DeleteChatModelConfig(ctx context.Context, modelConfigID uuid.U
 	return nil
 }
 
+// GetChatSystemPrompt returns the deployment-wide chat system prompt.
+func (c *Client) GetChatSystemPrompt(ctx context.Context) (ChatSystemPromptResponse, error) {
+	res, err := c.Request(ctx, http.MethodGet, "/api/experimental/chats/config/system-prompt", nil)
+	if err != nil {
+		return ChatSystemPromptResponse{}, err
+	}
+	defer res.Body.Close()
+	if res.StatusCode != http.StatusOK {
+		return ChatSystemPromptResponse{}, ReadBodyAsError(res)
+	}
+	var resp ChatSystemPromptResponse
+	return resp, json.NewDecoder(res.Body).Decode(&resp)
+}
+
+// UpdateChatSystemPrompt updates the deployment-wide chat system prompt.
+func (c *Client) UpdateChatSystemPrompt(ctx context.Context, req UpdateChatSystemPromptRequest) error {
+	res, err := c.Request(ctx, http.MethodPut, "/api/experimental/chats/config/system-prompt", req)
+	if err != nil {
+		return err
+	}
+	defer res.Body.Close()
+	if res.StatusCode != http.StatusNoContent {
+		return ReadBodyAsError(res)
+	}
+	return nil
+}
+
 // CreateChat creates a new chat.
 func (c *Client) CreateChat(ctx context.Context, req CreateChatRequest) (Chat, error) {
 	res, err := c.Request(ctx, http.MethodPost, "/api/experimental/chats", req)