sse: broadcast inbox_sorted on distributor runs

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

server/api/execute.ts

@@ -139,6 +139,11 @@ function emitJobProgress(jobId: number, seconds: number, total: number): void {
 	for (const l of jobListeners) l(line);
 }
 
+export function emitInboxSorted(result: { moved_to_queue: number; moved_to_review: number }): void {
+	const line = `event: inbox_sorted\ndata: ${JSON.stringify(result)}\n\n`;
+	for (const l of jobListeners) l(line);
+}
+
 /** Parse "Duration: HH:MM:SS.MS" from ffmpeg startup output. */
 function parseFFmpegDuration(line: string): number | null {
 	const match = line.match(/Duration:\s*(\d+):(\d+):(\d+)\.(\d+)/);