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/memories/write/src/phase1.rs

@@ -648,6 +648,11 @@ fn emit_metrics(context: &StageOneRequestContext, counts: &Stats) {
             token_usage.cached_input(),
             &[("token_type", "cached_input")],
         );
+        context.histogram(
+            MEMORY_PHASE_ONE_TOKEN_USAGE,
+            token_usage.cache_write_input_tokens.max(0),
+            &[("token_type", "cache_write_input")],
+        );
         context.histogram(
             MEMORY_PHASE_ONE_TOKEN_USAGE,
             token_usage.output_tokens.max(0),
@@ -821,6 +826,7 @@ mod tests {
                 token_usage: Some(TokenUsage {
                     input_tokens: 10,
                     cached_input_tokens: 2,
+                    cache_write_input_tokens: 0,
                     output_tokens: 3,
                     reasoning_output_tokens: 1,
                     total_tokens: 13,
@@ -831,6 +837,7 @@ mod tests {
                 token_usage: Some(TokenUsage {
                     input_tokens: 7,
                     cached_input_tokens: 1,
+                    cache_write_input_tokens: 0,
                     output_tokens: 2,
                     reasoning_output_tokens: 0,
                     total_tokens: 9,
@@ -851,6 +858,7 @@ mod tests {
             Some(TokenUsage {
                 input_tokens: 17,
                 cached_input_tokens: 3,
+                cache_write_input_tokens: 0,
                 output_tokens: 5,
                 reasoning_output_tokens: 1,
                 total_tokens: 22,