Fix log db batch flush flake (#19959)

## Why

The log DB writer batches tracing events before inserting them into
SQLite, but `tokio::time::interval` produces an immediate first tick.
That meant the inserter could flush the first accepted log entry before
`batch_size` was reached, making
`configured_batch_size_flushes_without_explicit_flush` timing-sensitive
in CI.

## What Changed

- Consume the interval's startup tick before entering the inserter loop,
so interval flushing starts after the configured delay.
- Remove the test's startup sleep, which was masking the race instead of
proving the batch-size behavior.

## Validation

- `cargo test -p codex-state`
- `cargo test -p codex-state
configured_batch_size_flushes_without_explicit_flush` passed 3
consecutive focused runs
- PR checks passed across `rust-ci`, Bazel, `ci`, `sdk`, `cargo-deny`,
Codespell, blob-size policy, and CLA

codex-rs/state/src/log_db.rs

@@ -367,6 +367,8 @@ async fn run_inserter(
 ) {
     let mut buffer = Vec::with_capacity(config.batch_size);
     let mut ticker = tokio::time::interval(config.flush_interval);
+    // Consume the immediate startup tick so entries flush after the interval.
+    ticker.tick().await;
     loop {
         tokio::select! {
             maybe_command = receiver.recv() => {
@@ -645,7 +647,6 @@ mod tests {
                 flush_interval: std::time::Duration::from_secs(60),
             },
         );
-        tokio::time::sleep(std::time::Duration::from_millis(10)).await;
 
         let guard = tracing_subscriber::registry()
             .with(