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/core/src/tasks/mod.rs

@@ -393,6 +393,7 @@ impl Session {
             codex.turn.reasoning_effort = %reasoning_effort,
             codex.turn.token_usage.input_tokens = field::Empty,
             codex.turn.token_usage.cached_input_tokens = field::Empty,
+            codex.turn.token_usage.cache_write_input_tokens = field::Empty,
             codex.turn.token_usage.non_cached_input_tokens = field::Empty,
             codex.turn.token_usage.output_tokens = field::Empty,
             codex.turn.token_usage.reasoning_output_tokens = field::Empty,
@@ -670,6 +671,9 @@ impl Session {
                 cached_input_tokens: (total_token_usage.cached_input_tokens
                     - token_usage_at_turn_start.cached_input_tokens)
                     .max(0),
+                cache_write_input_tokens: (total_token_usage.cache_write_input_tokens
+                    - token_usage_at_turn_start.cache_write_input_tokens)
+                    .max(0),
                 output_tokens: (total_token_usage.output_tokens
                     - token_usage_at_turn_start.output_tokens)
                     .max(0),
@@ -689,6 +693,10 @@ impl Session {
                 "codex.turn.token_usage.cached_input_tokens",
                 turn_token_usage.cached_input(),
             );
+            current_span.record(
+                "codex.turn.token_usage.cache_write_input_tokens",
+                turn_token_usage.cache_write_input_tokens,
+            );
             current_span.record(
                 "codex.turn.token_usage.non_cached_input_tokens",
                 turn_token_usage.non_cached_input(),
@@ -727,6 +735,11 @@ impl Session {
                 turn_token_usage.cached_input(),
                 &[("token_type", "cached_input"), tmp_mem],
             );
+            self.services.session_telemetry.histogram(
+                TURN_TOKEN_USAGE_METRIC,
+                turn_token_usage.cache_write_input_tokens,
+                &[("token_type", "cache_write_input"), tmp_mem],
+            );
             self.services.session_telemetry.histogram(
                 TURN_TOKEN_USAGE_METRIC,
                 turn_token_usage.output_tokens,