Add cache-write tokens to the raw response schema (#33500)

## What changed

Add `cacheWriteInputTokens` to the usage breakdown in the
`rawResponse/completed` JSON schema, defaulting it to zero. Update the
compaction and turn-start notification expectations for the expanded usage
breakdown.

GitOrigin-RevId: d9232b724d646b803c7f5a64c5daa311f77ad408

codex-rs/app-server-protocol/schema/json/v2/RawResponseCompletedNotification.json

@@ -3,6 +3,11 @@
   "definitions": {
     "TokenUsageBreakdown": {
       "properties": {
+        "cacheWriteInputTokens": {
+          "default": 0,
+          "format": "int64",
+          "type": "integer"
+        },
         "cachedInputTokens": {
           "format": "int64",
           "type": "integer"

codex-rs/app-server/tests/suite/v2/compaction.rs

@@ -345,6 +345,7 @@ async fn thread_compact_start_triggers_compaction_and_returns_empty_response() -
                 total_tokens: 200,
                 input_tokens: 200,
                 cached_input_tokens: 0,
+                cache_write_input_tokens: 0,
                 output_tokens: 0,
                 reasoning_output_tokens: 0,
             }),

codex-rs/app-server/tests/suite/v2/turn_start.rs

@@ -856,6 +856,7 @@ async fn turn_start_emits_raw_response_completed_with_upstream_usage() -> Result
                 total_tokens: 37,
                 input_tokens: 30,
                 cached_input_tokens: 11,
+                cache_write_input_tokens: 0,
                 output_tokens: 7,
                 reasoning_output_tokens: 3,
             }),