fix: handle all web_search actions and in progress invocations (#9960)

### Summary
- Parse all `web_search` tool actions (`search`, `find_in_page`,
`open_page`).
- Previously we only parsed + displayed `search`, which made the TUI
appear to pause when the other actions were being used.
- Show in progress `web_search` calls as `Searching the web`
  - Previously we only showed completed tool calls

<img width="308" height="149" alt="image"
src="https://github.com/user-attachments/assets/90a4e8ff-b06a-48ff-a282-b57b31121845"
/>

### Tests
Added + updated tests, tested locally

### Follow ups
Update VSCode extension to display these as well

codex-rs/exec/src/event_processor_with_human_output.rs

@@ -32,6 +32,7 @@ use codex_core::protocol::TurnCompleteEvent;
 use codex_core::protocol::TurnDiffEvent;
 use codex_core::protocol::WarningEvent;
 use codex_core::protocol::WebSearchEndEvent;
+use codex_core::web_search::web_search_detail;
 use codex_protocol::num_format::format_with_separators;
 use owo_colors::OwoColorize;
 use owo_colors::Style;
@@ -370,8 +371,20 @@ impl EventProcessor for EventProcessorWithHumanOutput {
                     }
                 }
             }
-            EventMsg::WebSearchEnd(WebSearchEndEvent { call_id: _, query }) => {
-                ts_msg!(self, "🌐 Searched: {query}");
+            EventMsg::WebSearchBegin(_) => {
+                ts_msg!(self, "🌐 Searching the web...");
+            }
+            EventMsg::WebSearchEnd(WebSearchEndEvent {
+                call_id: _,
+                query,
+                action,
+            }) => {
+                let detail = web_search_detail(Some(&action), &query);
+                if detail.is_empty() {
+                    ts_msg!(self, "🌐 Searched the web");
+                } else {
+                    ts_msg!(self, "🌐 Searched: {detail}");
+                }
             }
             EventMsg::PatchApplyBegin(PatchApplyBeginEvent {
                 call_id,
@@ -737,8 +750,7 @@ impl EventProcessor for EventProcessorWithHumanOutput {
                 );
             }
             EventMsg::ShutdownComplete => return CodexStatus::Shutdown,
-            EventMsg::WebSearchBegin(_)
-            | EventMsg::ExecApprovalRequest(_)
+            EventMsg::ExecApprovalRequest(_)
             | EventMsg::ApplyPatchApprovalRequest(_)
             | EventMsg::TerminalInteraction(_)
             | EventMsg::ExecCommandOutputDelta(_)

codex-rs/exec/src/event_processor_with_jsonl_output.rs

@@ -49,6 +49,7 @@ use codex_core::protocol::CollabCloseBeginEvent;
 use codex_core::protocol::CollabCloseEndEvent;
 use codex_core::protocol::CollabWaitingBeginEvent;
 use codex_core::protocol::CollabWaitingEndEvent;
+use codex_protocol::models::WebSearchAction;
 use codex_protocol::plan_tool::StepStatus;
 use codex_protocol::plan_tool::UpdatePlanArgs;
 use serde_json::Value as JsonValue;
@@ -66,6 +67,7 @@ pub struct EventProcessorWithJsonOutput {
     last_total_token_usage: Option<codex_core::protocol::TokenUsage>,
     running_mcp_tool_calls: HashMap<String, RunningMcpToolCall>,
     running_collab_tool_calls: HashMap<String, RunningCollabToolCall>,
+    running_web_search_calls: HashMap<String, String>,
     last_critical_error: Option<ThreadErrorEvent>,
 }
 
@@ -107,6 +109,7 @@ impl EventProcessorWithJsonOutput {
             last_total_token_usage: None,
             running_mcp_tool_calls: HashMap::new(),
             running_collab_tool_calls: HashMap::new(),
+            running_web_search_calls: HashMap::new(),
             last_critical_error: None,
         }
     }
@@ -138,7 +141,7 @@ impl EventProcessorWithJsonOutput {
             protocol::EventMsg::CollabCloseEnd(ev) => self.handle_collab_close_end(ev),
             protocol::EventMsg::PatchApplyBegin(ev) => self.handle_patch_apply_begin(ev),
             protocol::EventMsg::PatchApplyEnd(ev) => self.handle_patch_apply_end(ev),
-            protocol::EventMsg::WebSearchBegin(_) => Vec::new(),
+            protocol::EventMsg::WebSearchBegin(ev) => self.handle_web_search_begin(ev),
             protocol::EventMsg::WebSearchEnd(ev) => self.handle_web_search_end(ev),
             protocol::EventMsg::TokenCount(ev) => {
                 if let Some(info) = &ev.info {
@@ -195,11 +198,36 @@ impl EventProcessorWithJsonOutput {
         })]
     }
 
-    fn handle_web_search_end(&self, ev: &protocol::WebSearchEndEvent) -> Vec<ThreadEvent> {
+    fn handle_web_search_begin(&mut self, ev: &protocol::WebSearchBeginEvent) -> Vec<ThreadEvent> {
+        if self.running_web_search_calls.contains_key(&ev.call_id) {
+            return Vec::new();
+        }
+        let item_id = self.get_next_item_id();
+        self.running_web_search_calls
+            .insert(ev.call_id.clone(), item_id.clone());
         let item = ThreadItem {
-            id: self.get_next_item_id(),
+            id: item_id,
             details: ThreadItemDetails::WebSearch(WebSearchItem {
+                id: ev.call_id.clone(),
+                query: String::new(),
+                action: WebSearchAction::Other,
+            }),
+        };
+
+        vec![ThreadEvent::ItemStarted(ItemStartedEvent { item })]
+    }
+
+    fn handle_web_search_end(&mut self, ev: &protocol::WebSearchEndEvent) -> Vec<ThreadEvent> {
+        let item_id = self
+            .running_web_search_calls
+            .remove(&ev.call_id)
+            .unwrap_or_else(|| self.get_next_item_id());
+        let item = ThreadItem {
+            id: item_id,
+            details: ThreadItemDetails::WebSearch(WebSearchItem {
+                id: ev.call_id.clone(),
                 query: ev.query.clone(),
+                action: ev.action.clone(),
             }),
         };
 

codex-rs/exec/src/exec_events.rs

@@ -1,3 +1,4 @@
+use codex_protocol::models::WebSearchAction;
 use mcp_types::ContentBlock as McpContentBlock;
 use serde::Deserialize;
 use serde::Serialize;
@@ -280,7 +281,9 @@ pub struct McpToolCallItem {
 /// A web search request.
 #[derive(Debug, Clone, Serialize, Deserialize, PartialEq, TS)]
 pub struct WebSearchItem {
+    pub id: String,
     pub query: String,
+    pub action: WebSearchAction,
 }
 
 /// An error notification.