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/app-server-protocol/src/protocol/v2/thread.rs

@@ -1453,6 +1453,9 @@ pub struct TokenUsageBreakdown {
     pub input_tokens: i64,
     #[ts(type = "number")]
     pub cached_input_tokens: i64,
+    #[serde(default)]
+    #[ts(type = "number")]
+    pub cache_write_input_tokens: i64,
     #[ts(type = "number")]
     pub output_tokens: i64,
     #[ts(type = "number")]
@@ -1465,6 +1468,7 @@ impl From<CoreTokenUsage> for TokenUsageBreakdown {
             total_tokens: value.total_tokens,
             input_tokens: value.input_tokens,
             cached_input_tokens: value.cached_input_tokens,
+            cache_write_input_tokens: value.cache_write_input_tokens,
             output_tokens: value.output_tokens,
             reasoning_output_tokens: value.reasoning_output_tokens,
         }