feat: generate transcript and event-driven particle processing

This generates the transcript and shows the caption experience on the
client side for media particles. It also simplifies other side effects
that we must perform such as updating the `last_child_created_at` field
for stream and container particles.

js/src/lib/firestore-particles.ts

@@ -263,16 +263,6 @@ export async function updateParticle(
   });
 }
 
-export async function updateStreamLastChildAt(
-  docPath: string,
-): Promise<void> {
-  const particleRef = typedDoc(docPath);
-  await updateDoc(particleRef, {
-    last_child_created_at: serverTimestamp(),
-    updated_at: serverTimestamp(),
-  });
-}
-
 export async function updateStreamPlaybackMarker(
   docPath: string,
   humanId: string,