Track prompt cache write token usage (#33454)

## What changed

- Parse `cache_write_tokens` from response input token details and carry it through token usage aggregation.
- Expose `cache_write_input_tokens` in protocol, app-server, exec, and TypeScript SDK usage events, defaulting it to zero for compatibility with older payloads.
- Report cache-write usage in analytics, metrics, traces, and rollout data alongside existing cache-read usage.

## Testing

- Add coverage for response parsing, usage event output, aggregation, analytics, metrics, and telemetry fields.

GitOrigin-RevId: 634e4fbe3086a8923c0ee13b622573e7d9d221bd

codex-rs/exec/src/event_processor_with_jsonl_output.rs

@@ -121,6 +121,7 @@ impl EventProcessorWithJsonOutput {
         Usage {
             input_tokens: usage.total.input_tokens,
             cached_input_tokens: usage.total.cached_input_tokens,
+            cache_write_input_tokens: usage.total.cache_write_input_tokens,
             output_tokens: usage.total.output_tokens,
             reasoning_output_tokens: usage.total.reasoning_output_tokens,
         }

codex-rs/exec/src/exec_events.rs

@@ -63,6 +63,9 @@ pub struct Usage {
     pub input_tokens: i64,
     /// The number of cached input tokens used during the turn.
     pub cached_input_tokens: i64,
+    /// The number of input tokens written to the prompt cache during the turn.
+    #[serde(default)]
+    pub cache_write_input_tokens: i64,
     /// The number of output tokens used during the turn.
     pub output_tokens: i64,
     /// The number of reasoning output tokens used during the turn.

codex-rs/exec/tests/event_processor_with_json_output.rs

@@ -1231,6 +1231,7 @@ fn token_usage_update_is_emitted_on_turn_completion() {
                         total_tokens: 42,
                         input_tokens: 10,
                         cached_input_tokens: 3,
+                        cache_write_input_tokens: 4,
                         output_tokens: 29,
                         reasoning_output_tokens: 7,
                     },
@@ -1238,6 +1239,7 @@ fn token_usage_update_is_emitted_on_turn_completion() {
                         total_tokens: 42,
                         input_tokens: 10,
                         cached_input_tokens: 3,
+                        cache_write_input_tokens: 4,
                         output_tokens: 29,
                         reasoning_output_tokens: 7,
                     },
@@ -1275,6 +1277,7 @@ fn token_usage_update_is_emitted_on_turn_completion() {
                 usage: Usage {
                     input_tokens: 10,
                     cached_input_tokens: 3,
+                    cache_write_input_tokens: 4,
                     output_tokens: 29,
                     reasoning_output_tokens: 7,
                 },