Split plugin install discovery into list and request tools (#23372)

## Summary
- Add `list_available_plugins_to_install` as the inventory step for
plugin and connector install suggestions.
- Slim `request_plugin_install` so it only handles the actual
elicitation, instead of carrying the full discoverable list in its
prompt.
- Emit send-time telemetry when an install elicitation is dispatched,
including requested tool identity in the event payload.
- Emit install-result telemetry through `SessionTelemetry`, including
tool type, user response action, and completion status.
- Update registration and tests to cover the new two-step flow while
keeping the existing `tool_suggest` feature gate unchanged.

## Testing
- `just fmt`
- `cargo test -p codex-tools`
- `cargo test -p codex-core request_plugin_install`
- `cargo test -p codex-core list_available_plugins_to_install`
- `cargo test -p codex-core
install_suggestion_tools_can_be_registered_without_search_tool`
- `cargo test -p codex-otel
manager_records_plugin_install_suggestion_metric`
- `cargo test -p codex-otel
manager_records_plugin_install_elicitation_sent_metric`
- `just fix -p codex-core`
- `just fix -p codex-tools`
- `just fix -p codex-otel`
- `cargo check -p codex-core`

codex-rs/tools/src/lib.rs

@@ -71,6 +71,8 @@ pub use tool_discovery::DiscoverablePluginInfo;
 pub use tool_discovery::DiscoverableTool;
 pub use tool_discovery::DiscoverableToolAction;
 pub use tool_discovery::DiscoverableToolType;
+pub use tool_discovery::LIST_AVAILABLE_PLUGINS_TO_INSTALL_TOOL_NAME;
+pub use tool_discovery::ListAvailablePluginsToInstallResult;
 pub use tool_discovery::REQUEST_PLUGIN_INSTALL_TOOL_NAME;
 pub use tool_discovery::RequestPluginInstallEntry;
 pub use tool_discovery::TOOL_SEARCH_DEFAULT_LIMIT;

codex-rs/tools/src/tool_discovery.rs

@@ -5,6 +5,7 @@ use serde::Serialize;
 const TUI_CLIENT_NAME: &str = "codex-tui";
 pub const TOOL_SEARCH_TOOL_NAME: &str = "tool_search";
 pub const TOOL_SEARCH_DEFAULT_LIMIT: usize = 8;
+pub const LIST_AVAILABLE_PLUGINS_TO_INSTALL_TOOL_NAME: &str = "list_available_plugins_to_install";
 pub const REQUEST_PLUGIN_INSTALL_TOOL_NAME: &str = "request_plugin_install";
 
 #[derive(Clone, Debug, PartialEq, Eq)]
@@ -99,7 +100,7 @@ pub struct DiscoverablePluginInfo {
     pub app_connector_ids: Vec<String>,
 }
 
-#[derive(Clone, Debug, PartialEq, Eq)]
+#[derive(Clone, Debug, Serialize, PartialEq, Eq)]
 pub struct RequestPluginInstallEntry {
     pub id: String,
     pub name: String,
@@ -110,6 +111,11 @@ pub struct RequestPluginInstallEntry {
     pub app_connector_ids: Vec<String>,
 }
 
+#[derive(Clone, Debug, Serialize, PartialEq, Eq)]
+pub struct ListAvailablePluginsToInstallResult {
+    pub tools: Vec<RequestPluginInstallEntry>,
+}
+
 pub fn collect_request_plugin_install_entries(
     discoverable_tools: &[DiscoverableTool],
 ) -> Vec<RequestPluginInstallEntry> {