feat: add calcOffsetSecs utility to compute accurate elapsed seconds for broadcasts

k-tv-frontend/app/(main)/tv/page.tsx

@@ -16,6 +16,7 @@ import {
   useStreamUrl,
   fmtTime,
   calcProgress,
+  calcOffsetSecs,
   minutesUntil,
   toScheduleSlots,
   findNextSlot,
@@ -223,7 +224,7 @@ export default function TvPage() {
           ref={videoRef}
           src={streamUrl}
           className="absolute inset-0 h-full w-full"
-          initialOffset={broadcast?.offset_secs ?? 0}
+          initialOffset={broadcast ? calcOffsetSecs(broadcast.slot.start_at) : 0}
           onStreamError={handleStreamError}
         />
       );