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.

coderd/database/queries/chats.sql

@@ -373,6 +373,11 @@ WHERE
         WHEN sqlc.narg('label_filter')::jsonb IS NOT NULL THEN chats.labels @> sqlc.narg('label_filter')::jsonb
         ELSE true
     END
+    -- Paginate over root chats only. Children are fetched
+    -- separately via GetChildChatsByParentIDs and embedded under
+    -- each parent. Other callers that need the full set should
+    -- use a narrower query (e.g. GetChatsByWorkspaceIDs).
+    AND chats.parent_chat_id IS NULL
     -- Authorize Filter clause will be injected below in GetAuthorizedChats
     -- @authorize_filter
 ORDER BY
@@ -390,6 +395,32 @@ LIMIT
     -- Default to 50 to prevent accidental excessively large queries.
     COALESCE(NULLIF(@limit_opt :: int, 0), 50);
 
+-- name: GetChildChatsByParentIDs :many
+-- Fetches child chats of the given parents, optionally filtered by
+-- archive state (NULL = all, true/false = match). The archive
+-- invariant (parent archived implies child archived) is enforced
+-- at write time, not here.
+SELECT
+    sqlc.embed(chats),
+    EXISTS (
+        SELECT 1 FROM chat_messages cm
+        WHERE cm.chat_id = chats.id
+            AND cm.role = 'assistant'
+            AND cm.deleted = false
+            AND cm.id > COALESCE(chats.last_read_message_id, 0)
+    ) AS has_unread
+FROM
+    chats
+WHERE
+    chats.parent_chat_id = ANY(@parent_ids :: uuid[])
+    AND CASE
+        WHEN sqlc.narg('archived') :: boolean IS NULL THEN true
+        ELSE chats.archived = sqlc.narg('archived') :: boolean
+    END
+ORDER BY
+    chats.created_at ASC,
+    chats.id ASC;
+
 -- name: InsertChat :one
 INSERT INTO chats (
     organization_id,