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/protocol/src/protocol.rs

@@ -2047,6 +2047,9 @@ pub struct TokenUsage {
     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")]
@@ -2247,6 +2250,7 @@ impl TokenUsage {
     pub fn add_assign(&mut self, other: &TokenUsage) {
         self.input_tokens += other.input_tokens;
         self.cached_input_tokens += other.cached_input_tokens;
+        self.cache_write_input_tokens += other.cache_write_input_tokens;
         self.output_tokens += other.output_tokens;
         self.reasoning_output_tokens += other.reasoning_output_tokens;
         self.total_tokens += other.total_tokens;
@@ -6214,6 +6218,7 @@ mod tests {
         let last = Some(TokenUsage {
             input_tokens: 10,
             cached_input_tokens: 0,
+            cache_write_input_tokens: 0,
             output_tokens: 0,
             reasoning_output_tokens: 0,
             total_tokens: 10,
@@ -6235,6 +6240,7 @@ mod tests {
         let last = Some(TokenUsage {
             input_tokens: 10,
             cached_input_tokens: 0,
+            cache_write_input_tokens: 0,
             output_tokens: 0,
             reasoning_output_tokens: 0,
             total_tokens: 10,