[codex-analytics] add protocol-native turn timestamps (#16638)

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[//]: # (BEGIN SAPLING FOOTER)
Stack created with [Sapling](https://sapling-scm.com). Best reviewed
with [ReviewStack](https://reviewstack.dev/openai/codex/pull/16638).
* #16870
* #16706
* #16659
* #16641
* #16640
* __->__ #16638

codex-rs/app-server/src/in_process.rs

@@ -826,6 +826,9 @@ mod tests {
                     items: Vec::new(),
                     status: TurnStatus::Completed,
                     error: None,
+                    started_at: None,
+                    completed_at: Some(0),
+                    duration_ms: None,
                 },
             })
         ));