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.

TODO.md

@@ -1,6 +1 @@
-- [ ] When opening a codex sub agent, the message gets input to the field, but the message is never submitted.
-  - This appears to be inconsistent. Sometimes it works, sometimes it doesn't. Might be because of popups on codex sub agents?
-  - Question: when it fails, is a Codex startup popup visible (trust/workspace, auth/model selection, permissions), or is the normal composer focused?
-  - Question: if the message is sitting in the composer, does pressing Enter once manually submit it, or does something else need to be dismissed first?
-  - Question: does this happen with short one-line prompts as well as long/multiline sub-agent instructions?
 - [ ] The per-tab agent summary text should display below the tab always, not just when the tab is focused.