Give injected agent submit Enter a longer settle delay

The trailing CR that submits orchestrator-injected input was written
only 15ms after the body, inside TUI agents' paste-coalescing window,
so codex (and other paste-detecting agents) intermittently swallowed it
as a newline and left the message composed but unsent. Centralize the
per-piece timing in a pure pieceWriteDelay helper: keep 15ms between
body lines but give the final lone Enter a 100ms settle gap so the
agent closes the preceding burst and registers the CR as submit. Covers
send_input, send_message, timers, and the spawn initial prompt (all go
through writeInput).

Resolves the codex composer-submit TODO item.

internal/app/child.go

@@ -26,6 +26,11 @@ import (
 // false positives (timestamps, exit codes, etc.).
 var portRegex = regexp.MustCompile(`https?://[^\s:/]+:(\d{2,5})(?:/[^\s]*)?`)
 
+const (
+	agentInterPieceDelay   = 15 * time.Millisecond
+	agentSubmitSettleDelay = 100 * time.Millisecond
+)
+
 type ChildStatus string
 
 const (
@@ -642,8 +647,8 @@ func (c *Child) writeInput(b []byte) error {
 		return err
 	}
 	for i, piece := range pieces {
-		if i > 0 {
-			time.Sleep(15 * time.Millisecond)
+		if delay := pieceWriteDelay(i, len(pieces), piece); delay > 0 {
+			time.Sleep(delay)
 		}
 		if _, err := pty.Write(piece); err != nil {
 			return err
@@ -659,6 +664,20 @@ func inputWritePieces(kind ChildKind, b []byte) [][]byte {
 	return splitOnEnter(b)
 }
 
+func pieceWriteDelay(index, total int, piece []byte) time.Duration {
+	if index == 0 {
+		return 0
+	}
+	if index == total-1 && isLoneEnter(piece) {
+		return agentSubmitSettleDelay
+	}
+	return agentInterPieceDelay
+}
+
+func isLoneEnter(piece []byte) bool {
+	return len(piece) == 1 && (piece[0] == '\r' || piece[0] == '\n')
+}
+
 func mintIdentity() string {
 	var buf [12]byte
 	_, _ = rand.Read(buf[:])