Use Tokio's clock for TUI paste timing (#47881)

## Why

Paste input classification and asynchronous flush deadlines need to share a clock, including when Tokio time is paused in tests.

## What changed

Use Tokio's clock for chat composer paste timing and startup draft newline tracking, converting to `std::time::Instant` where existing composer helpers require it.

## Testing

Run the existing startup draft multiline paste test with `start_paused = true`. It checks that non-bracketed pastes preserve newlines without submitting the draft.

GitOrigin-RevId: 73bac963204473d85e7395781e0df966ecc92801

codex-rs/tui/src/startup_draft_input.rs

@@ -4,7 +4,7 @@
 //! preserved, protected screens do not consume draft input, and confirmation never removes text.
 
 use std::io;
-use std::time::Instant;
+use tokio::time::Instant;
 
 use crossterm::event::KeyCode;
 use crossterm::event::KeyEvent;