[codex] Send realtime transcript deltas on handoff (#18761)

## Summary
- Track how many realtime transcript entries have already been attached
to a background-agent handoff.
- Attach only entries added since the previous handoff as
`<transcript_delta>` instead of resending the accumulated transcript
snapshot.
- Update the realtime integration test so the second delegation carries
only the second transcript delta.

## Validation
- `just fmt`
- `cargo test -p codex-api`
- `cargo test -p codex-core
inbound_handoff_request_sends_transcript_delta_after_each_handoff`
- `cargo build -p codex-cli -p codex-app-server`

## Manual testing
Built local debug binaries at:
- `codex-rs/target/debug/codex`
- `codex-rs/target/debug/codex-app-server`

codex-rs/codex-api/src/endpoint/realtime_websocket/methods.rs

@@ -217,6 +217,7 @@ pub struct RealtimeWebsocketEvents {
 #[derive(Default)]
 struct ActiveTranscriptState {
     entries: Vec<RealtimeTranscriptEntry>,
+    last_handoff_entry_count: usize,
     new_input_entry: bool,
     new_output_entry: bool,
 }
@@ -459,7 +460,10 @@ impl RealtimeWebsocketEvents {
             }
             RealtimeEvent::HandoffRequested(handoff) => {
                 append_handoff_input(&mut active_transcript.entries, &handoff.input_transcript);
-                handoff.active_transcript = active_transcript.entries.clone();
+                handoff.active_transcript = active_transcript.entries
+                    [active_transcript.last_handoff_entry_count..]
+                    .to_vec();
+                active_transcript.last_handoff_entry_count = active_transcript.entries.len();
                 active_transcript.new_input_entry = true;
                 active_transcript.new_output_entry = true;
             }