[tool_suggest] More prompt polishes. (#20566)

Tool suggest still misfires when model needs tool_search, updating the
prompts to further disambiguate it:

- [x] rename it from `tool_suggest` to `request_plugin_install`
- [x] rephrase "suggestion" to "install" in the tool descriptions.
- [x] disambiguate "the tool" vs "the plugin/connector". 

Tested with the Codex App and verified it still works.

codex-rs/tools/src/lib.rs

@@ -13,6 +13,7 @@ mod local_tool;
 mod mcp_resource_tool;
 mod mcp_tool;
 mod plan_tool;
+mod request_plugin_install;
 mod request_user_input_tool;
 mod responses_api;
 mod tool_config;
@@ -21,7 +22,6 @@ mod tool_discovery;
 mod tool_registry_plan;
 mod tool_registry_plan_types;
 mod tool_spec;
-mod tool_suggest;
 mod utility_tool;
 mod view_image;
 
@@ -80,6 +80,15 @@ pub use mcp_resource_tool::create_read_mcp_resource_tool;
 pub use mcp_tool::mcp_call_tool_result_output_schema;
 pub use mcp_tool::parse_mcp_tool;
 pub use plan_tool::create_update_plan_tool;
+pub use request_plugin_install::REQUEST_PLUGIN_INSTALL_APPROVAL_KIND_VALUE;
+pub use request_plugin_install::REQUEST_PLUGIN_INSTALL_PERSIST_ALWAYS_VALUE;
+pub use request_plugin_install::REQUEST_PLUGIN_INSTALL_PERSIST_KEY;
+pub use request_plugin_install::RequestPluginInstallArgs;
+pub use request_plugin_install::RequestPluginInstallMeta;
+pub use request_plugin_install::RequestPluginInstallResult;
+pub use request_plugin_install::all_requested_connectors_picked_up;
+pub use request_plugin_install::build_request_plugin_install_elicitation_request;
+pub use request_plugin_install::verified_connector_install_completed;
 pub use request_user_input_tool::REQUEST_USER_INPUT_TOOL_NAME;
 pub use request_user_input_tool::create_request_user_input_tool;
 pub use request_user_input_tool::normalize_request_user_input_args;
@@ -110,18 +119,18 @@ pub use tool_discovery::DiscoverablePluginInfo;
 pub use tool_discovery::DiscoverableTool;
 pub use tool_discovery::DiscoverableToolAction;
 pub use tool_discovery::DiscoverableToolType;
+pub use tool_discovery::REQUEST_PLUGIN_INSTALL_TOOL_NAME;
+pub use tool_discovery::RequestPluginInstallEntry;
 pub use tool_discovery::TOOL_SEARCH_DEFAULT_LIMIT;
 pub use tool_discovery::TOOL_SEARCH_TOOL_NAME;
-pub use tool_discovery::TOOL_SUGGEST_TOOL_NAME;
 pub use tool_discovery::ToolSearchResultSource;
 pub use tool_discovery::ToolSearchSource;
 pub use tool_discovery::ToolSearchSourceInfo;
-pub use tool_discovery::ToolSuggestEntry;
+pub use tool_discovery::collect_request_plugin_install_entries;
 pub use tool_discovery::collect_tool_search_source_infos;
-pub use tool_discovery::collect_tool_suggest_entries;
+pub use tool_discovery::create_request_plugin_install_tool;
 pub use tool_discovery::create_tool_search_tool;
-pub use tool_discovery::create_tool_suggest_tool;
-pub use tool_discovery::filter_tool_suggest_discoverable_tools_for_client;
+pub use tool_discovery::filter_request_plugin_install_discoverable_tools_for_client;
 pub use tool_discovery::tool_search_result_source_to_loadable_tool_spec;
 pub use tool_registry_plan::build_tool_registry_plan;
 pub use tool_registry_plan_types::ToolHandlerKind;
@@ -140,15 +149,6 @@ pub use tool_spec::create_image_generation_tool;
 pub use tool_spec::create_local_shell_tool;
 pub use tool_spec::create_tools_json_for_responses_api;
 pub use tool_spec::create_web_search_tool;
-pub use tool_suggest::TOOL_SUGGEST_APPROVAL_KIND_VALUE;
-pub use tool_suggest::TOOL_SUGGEST_PERSIST_ALWAYS_VALUE;
-pub use tool_suggest::TOOL_SUGGEST_PERSIST_KEY;
-pub use tool_suggest::ToolSuggestArgs;
-pub use tool_suggest::ToolSuggestMeta;
-pub use tool_suggest::ToolSuggestResult;
-pub use tool_suggest::all_suggested_connectors_picked_up;
-pub use tool_suggest::build_tool_suggestion_elicitation_request;
-pub use tool_suggest::verified_connector_suggestion_completed;
 pub use utility_tool::create_list_dir_tool;
 pub use utility_tool::create_test_sync_tool;
 pub use view_image::ViewImageToolOptions;