fix(broadcast): port corrected org-root CTE from org_scope.go (#1959)

workspace_broadcast.go used the OLD org-root CTE shape that carried
`id AS root_id` from the recursive seed. For a non-root sender, this
resolved the org root to the sender's own ID instead of the topmost
ancestor, causing broadcast under-delivery (missed the rest of the org
subtree).

Replace the inline CTE with the shared `orgRootID` helper from
org_scope.go (commit from #1954), which selects `id AS root_id` only
from the parentless row — the actual org root.

Fixes #1959

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

workspace-server/internal/handlers/workspace_broadcast.go

@@ -82,19 +82,7 @@ func (h *BroadcastHandler) Broadcast(c *gin.Context) {
 	// Find the sender's org root by walking the parent_id chain.
 	// Workspaces with parent_id = NULL are org roots; every other workspace
 	// belongs to the org identified by its topmost ancestor.
-	var orgRootID string
-	err = db.DB.QueryRowContext(ctx, `
-		WITH RECURSIVE org_chain AS (
-			SELECT id, parent_id, id AS root_id
-			FROM workspaces
-			WHERE id = $1
-			UNION ALL
-			SELECT w.id, w.parent_id, c.root_id
-			FROM workspaces w
-			JOIN org_chain c ON w.id = c.parent_id
-		)
-		SELECT root_id FROM org_chain WHERE parent_id IS NULL LIMIT 1
-	`, senderID).Scan(&orgRootID)
+	rootID, err := orgRootID(ctx, db.DB, senderID)
 	if err != nil {
 		log.Printf("Broadcast: org root lookup for %s: %v", senderID, err)
 		c.JSON(http.StatusInternalServerError, gin.H{"error": "internal error"})
@@ -121,7 +109,7 @@ func (h *BroadcastHandler) Broadcast(c *gin.Context) {
 			  SELECT 1 FROM workspaces w
 			  WHERE w.id = c.id AND w.status != 'removed'
 		  )
-	`, orgRootID, senderID)
+	`, rootID, senderID)
 	if err != nil {
 		log.Printf("Broadcast: recipient query failed for %s: %v", senderID, err)
 		c.JSON(http.StatusInternalServerError, gin.H{"error": "internal error"})