feat: show agent badge on workspace list (#23453)

- Adds `GET /api/experimental/chats/by-workspace` endpoint that returns
workspace_id → latest chat_id mapping
- Modifies FE to fetch this alongside the workspace list, gated on
`agents` experiment and render an "Agent" badge similar to the existing
"Task" badge in `WorkspacesTable`
- Badge links to the "latest chat" linked to the given workspace.

Notes:
- Intentionally uses `fetchWithPostFilter` for RBAC to decouple from
workspaces API — will migrate to `workspaces_expanded` view later.
- If users have multiple chats linked to the same workspace, the badge
will link to the most recently updated one.

> 🤖 This PR was created with the help of Coder Agents, and has been
reviewed by my human. 🧑‍💻

coderd/database/queries.sql.go

@@ -5153,6 +5153,58 @@ func (q *sqlQuerier) GetChats(ctx context.Context, arg GetChatsParams) ([]Chat,
 	return items, nil
 }
 
+const getChatsByWorkspaceIDs = `-- name: GetChatsByWorkspaceIDs :many
+SELECT id, owner_id, workspace_id, title, status, worker_id, started_at, heartbeat_at, created_at, updated_at, parent_chat_id, root_chat_id, last_model_config_id, archived, last_error, mode, mcp_server_ids, labels, build_id, agent_id
+FROM chats
+WHERE archived = false
+  AND workspace_id = ANY($1::uuid[])
+ORDER BY workspace_id, updated_at DESC
+`
+
+func (q *sqlQuerier) GetChatsByWorkspaceIDs(ctx context.Context, ids []uuid.UUID) ([]Chat, error) {
+	rows, err := q.db.QueryContext(ctx, getChatsByWorkspaceIDs, pq.Array(ids))
+	if err != nil {
+		return nil, err
+	}
+	defer rows.Close()
+	var items []Chat
+	for rows.Next() {
+		var i Chat
+		if err := rows.Scan(
+			&i.ID,
+			&i.OwnerID,
+			&i.WorkspaceID,
+			&i.Title,
+			&i.Status,
+			&i.WorkerID,
+			&i.StartedAt,
+			&i.HeartbeatAt,
+			&i.CreatedAt,
+			&i.UpdatedAt,
+			&i.ParentChatID,
+			&i.RootChatID,
+			&i.LastModelConfigID,
+			&i.Archived,
+			&i.LastError,
+			&i.Mode,
+			pq.Array(&i.MCPServerIDs),
+			&i.Labels,
+			&i.BuildID,
+			&i.AgentID,
+		); err != nil {
+			return nil, err
+		}
+		items = append(items, i)
+	}
+	if err := rows.Close(); err != nil {
+		return nil, err
+	}
+	if err := rows.Err(); err != nil {
+		return nil, err
+	}
+	return items, nil
+}
+
 const getLastChatMessageByRole = `-- name: GetLastChatMessageByRole :one
 SELECT
     id, chat_id, model_config_id, created_at, role, content, visibility, input_tokens, output_tokens, total_tokens, reasoning_tokens, cache_creation_tokens, cache_read_tokens, context_limit, compressed, created_by, content_version, total_cost_micros, runtime_ms, deleted, provider_response_id