feat(coderd): add q search parameter to chats endpoint (#22913)

Replace the standalone `?archived=` query parameter on the chats listing
endpoint with a `?q=` search parameter, consistent with how workspaces,
tasks, templates, and other list endpoints work.

The `q` parameter uses the standard `key:value` search syntax parsed by
the `searchquery` package. Currently supports:

- `archived:true/false` (default: `false`, hides archived chats)

When `q` is empty or omits the archived filter, archived chats are
excluded by default. This is a behavioral change — the previous API
returned all chats (including archived) when no filter was specified.

### Changes

**Backend:**
- Add `searchquery.Chats()` parser following the same pattern as
`Tasks()`, `Workspaces()`, etc.
- Update `listChats` handler to read `q` instead of `archived`
- Update `codersdk.ListChatsOptions` to use `Q string` instead of
`Archived *bool`

**Frontend:**
- Update `getChats` API method to accept `q` parameter
- Update `infiniteChats` query to pass `q` instead of `archived`

**Tests:**
- Add `TestSearchChats` unit tests for the parser
- Update existing archive/unarchive integration tests to use `Q:
"archived:true"` syntax

codersdk/chats.go

@@ -551,7 +551,7 @@ type chatStreamEnvelope struct {
 
 // ListChatsOptions are optional parameters for ListChats.
 type ListChatsOptions struct {
-	Archived *bool
+	Query string
 	Pagination
 }
 
@@ -560,10 +560,10 @@ func (c *Client) ListChats(ctx context.Context, opts *ListChatsOptions) ([]Chat,
 	var reqOpts []RequestOption
 	if opts != nil {
 		reqOpts = append(reqOpts, opts.Pagination.asRequestOption())
-		if opts.Archived != nil {
+		if opts.Query != "" {
 			reqOpts = append(reqOpts, func(r *http.Request) {
 				q := r.URL.Query()
-				q.Set("archived", fmt.Sprintf("%t", *opts.Archived))
+				q.Set("q", opts.Query)
 				r.URL.RawQuery = q.Encode()
 			})
 		}