feat(chats): archive chats instead of hard-deleting them (#22406)

## Summary

The UI has always labeled the action as "Archive agent" but the backend
was performing a hard `DELETE`, permanently destroying chats and all
their messages.

This change replaces the hard delete with a soft archive, consistent
with the pattern used by template versions.

## Changes

### Database
- **Migration 000423**: Add `archived boolean DEFAULT false NOT NULL`
column to `chats` table
- Replace `DeleteChatByID` query with `ArchiveChatByID` (`UPDATE SET
archived = true`)
- Add `UnarchiveChatByID` query (`UPDATE SET archived = false`)
- Filter archived chats from `GetChatsByOwnerID` (`WHERE archived =
false`)

### API
- Remove `DELETE /api/experimental/chats/{chat}`
- Add `POST /api/experimental/chats/{chat}/archive` — archives a chat
and all its descendants
- Add `POST /api/experimental/chats/{chat}/unarchive` — unarchives a
single chat (API only, no UI yet)

### Backend
- `archiveChatTree()` recursively archives child chats (replaces
`deleteChatTree()` which hard-deleted)
- Chat daemon's `ArchiveChat()` archives the full chat tree in a
transaction
- Authorization uses `ActionUpdate` instead of `ActionDelete`

### SDK
- Replace `DeleteChat()` with `ArchiveChat()` and `UnarchiveChat()`
- Add `Archived` field to `Chat` struct

### Frontend
- `archiveChat` API call uses `POST .../archive` instead of `DELETE`
- No UI changes — the "Archive agent" button now actually archives
instead of deleting

## Design Decision

This follows the **template version archive pattern** (Pattern B in the
codebase):
- `archived boolean` column (not `deleted boolean`)
- Dedicated `POST .../archive` and `POST .../unarchive` routes (not
repurposing `DELETE`)
- Reversible — users can unarchive via the API (UI for this will come
later)

codersdk/chats.go

@@ -41,6 +41,7 @@ type Chat struct {
 	DiffStatus        *ChatDiffStatus `json:"diff_status,omitempty"`
 	CreatedAt         time.Time       `json:"created_at" format:"date-time"`
 	UpdatedAt         time.Time       `json:"updated_at" format:"date-time"`
+	Archived          bool            `json:"archived"`
 }
 
 // ChatMessage represents a single message in a chat.
@@ -780,9 +781,20 @@ func (c *Client) GetChat(ctx context.Context, chatID uuid.UUID) (ChatWithMessage
 	return chat, json.NewDecoder(res.Body).Decode(&chat)
 }
 
-// DeleteChat deletes a chat by ID.
-func (c *Client) DeleteChat(ctx context.Context, chatID uuid.UUID) error {
-	res, err := c.Request(ctx, http.MethodDelete, fmt.Sprintf("/api/experimental/chats/%s", chatID), nil)
+func (c *Client) ArchiveChat(ctx context.Context, chatID uuid.UUID) error {
+	res, err := c.Request(ctx, http.MethodPost, fmt.Sprintf("/api/experimental/chats/%s/archive", chatID), nil)
+	if err != nil {
+		return err
+	}
+	defer res.Body.Close()
+	if res.StatusCode != http.StatusNoContent {
+		return ReadBodyAsError(res)
+	}
+	return nil
+}
+
+func (c *Client) UnarchiveChat(ctx context.Context, chatID uuid.UUID) error {
+	res, err := c.Request(ctx, http.MethodPost, fmt.Sprintf("/api/experimental/chats/%s/unarchive", chatID), nil)
 	if err != nil {
 		return err
 	}