[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/core/src/session/turn.rs

@@ -97,7 +97,7 @@ use codex_protocol::protocol::TurnDiffEvent;
 use codex_protocol::protocol::WarningEvent;
 use codex_protocol::user_input::UserInput;
 use codex_tools::ToolName;
-use codex_tools::filter_tool_suggest_discoverable_tools_for_client;
+use codex_tools::filter_request_plugin_install_discoverable_tools_for_client;
 use codex_utils_stream_parser::AssistantTextChunk;
 use codex_utils_stream_parser::AssistantTextStreamParser;
 use codex_utils_stream_parser::ProposedPlanSegment;
@@ -1170,7 +1170,7 @@ pub(crate) async fn built_tools(
             )
             .await
             .map(|discoverable_tools| {
-                filter_tool_suggest_discoverable_tools_for_client(
+                filter_request_plugin_install_discoverable_tools_for_client(
                     discoverable_tools,
                     turn_context.app_server_client_name.as_deref(),
                 )