Record web search result payload sizes (#33851)

## What changed

Record the serialized size of structured web search results in the
`codex.web_search.results.payload_bytes` histogram when telemetry is available.

GitOrigin-RevId: 6e87e21d3ae7de03079ecaf6cd08f9770dffc436

codex-rs/Cargo.lock

@@ -4454,6 +4454,7 @@ dependencies = [
  "codex-login",
  "codex-model-provider",
  "codex-model-provider-info",
+ "codex-otel",
  "codex-protocol",
  "codex-tools",
  "http 1.4.0",

codex-rs/ext/web-search/Cargo.toml

@@ -20,6 +20,7 @@ codex-extension-items = { workspace = true }
 codex-login = { workspace = true }
 codex-model-provider = { workspace = true }
 codex-model-provider-info = { workspace = true }
+codex-otel = { workspace = true }
 codex-protocol = { workspace = true }
 codex-tools = { workspace = true }
 http = { workspace = true }

codex-rs/ext/web-search/src/tool.rs

@@ -40,6 +40,7 @@ use crate::schema::commands_schema;
 pub(crate) const WEB_NAMESPACE: &str = "web";
 pub(crate) const RUN_TOOL_NAME: &str = "run";
 const WEB_RUN_DESCRIPTION: &str = include_str!("../web_run_description.md");
+const RESULTS_PAYLOAD_BYTES_METRIC: &str = "codex.web_search.results.payload_bytes";
 
 pub(crate) struct WebSearchTool {
     pub(crate) session_id: String,
@@ -140,6 +141,13 @@ impl WebSearchTool {
             .map_err(|err| FunctionCallError::Fatal(err.to_string()))?;
         let output = response.output;
         let results = response.results;
+        if let Some(results) = results.as_ref()
+            && let Some(metrics) = codex_otel::global()
+            && let Ok(payload) = serde_json::to_vec(results)
+        {
+            let payload_bytes = i64::try_from(payload.len()).unwrap_or(i64::MAX);
+            let _ = metrics.histogram(RESULTS_PAYLOAD_BYTES_METRIC, payload_bytes, &[]);
+        }
         let legacy_action = match &command_action {
             WebSearchAction::Search { query, queries } => CoreWebSearchAction::Search {
                 query: query.clone(),