fix: exclude subagent chats from sidebar pagination (#24404)

GetChats now returns only root chats (parent_chat_id IS NULL).
A new GetChildChatsByParentIDs query fetches children for visible
roots and embeds them in each parent's Children field. The
singular getChat endpoint does the same.

Archive invariant is one-way: parent archived implies child
archived. Parent archive/unarchive cascades via root_chat_id.
Individual child archive is permitted; child unarchive while the
parent is archived is rejected atomically (row lock on child,
re-read parent inside the transaction). Embedded children are
filtered by the caller's archive state so individually-archived
children stay hidden from active-parent views.

Gitsync MarkStale uses GetChatsByWorkspaceIDs directly;
MarkStaleParams.OwnerID removed (dead after the switch).

Frontend: buildChatTree reads from the embedded children field,
WebSocket handlers route child events into the parent's children
array, and archiving a child strips it from the parent cache.

codersdk/chats.go

@@ -95,6 +95,12 @@ type Chat struct {
 	LastInjectedContext []ChatMessagePart `json:"last_injected_context,omitempty"`
 	Warnings            []string          `json:"warnings,omitempty"`
 	ClientType          ChatClientType    `json:"client_type"`
+	// Children holds child (subagent) chats nested under this root
+	// chat. Always initialized to an empty slice so the JSON field
+	// is present as []. Child chats cannot create their own
+	// subagents, so nesting depth is capped at 1 and this slice is
+	// always empty for child chats.
+	Children []Chat `json:"children"`
 }
 
 // ChatFileMetadata contains lightweight metadata about a file