Dividing UserMsgs into categories to send it back to the tui (#3127)

This PR does the following:

- divides user msgs into 3 categories: plain, user instructions, and
environment context
- Centralizes adding user instructions and environment context to a
degree
- Improve the integration testing

Building on top of #3123

Specifically this
[comment](https://github.com/openai/codex/pull/3123#discussion_r2319885089).
We need to send the user message while ignoring the User Instructions
and Environment Context we attach.

codex-rs/core/src/client_common.rs

@@ -6,7 +6,6 @@ use codex_apply_patch::APPLY_PATCH_TOOL_INSTRUCTIONS;
 use codex_protocol::config_types::ReasoningEffort as ReasoningEffortConfig;
 use codex_protocol::config_types::ReasoningSummary as ReasoningSummaryConfig;
 use codex_protocol::config_types::Verbosity as VerbosityConfig;
-use codex_protocol::models::ContentItem;
 use codex_protocol::models::ResponseItem;
 use futures::Stream;
 use serde::Serialize;
@@ -20,10 +19,6 @@ use tokio::sync::mpsc;
 /// with this content.
 const BASE_INSTRUCTIONS: &str = include_str!("../prompt.md");
 
-/// wraps user instructions message in a tag for the model to parse more easily.
-const USER_INSTRUCTIONS_START: &str = "<user_instructions>\n\n";
-const USER_INSTRUCTIONS_END: &str = "\n\n</user_instructions>";
-
 /// API request payload for a single model turn
 #[derive(Default, Debug, Clone)]
 pub struct Prompt {
@@ -68,17 +63,6 @@ impl Prompt {
     pub(crate) fn get_formatted_input(&self) -> Vec<ResponseItem> {
         self.input.clone()
     }
-
-    /// Creates a formatted user instructions message from a string
-    pub(crate) fn format_user_instructions_message(ui: &str) -> ResponseItem {
-        ResponseItem::Message {
-            id: None,
-            role: "user".to_string(),
-            content: vec![ContentItem::InputText {
-                text: format!("{USER_INSTRUCTIONS_START}{ui}{USER_INSTRUCTIONS_END}"),
-            }],
-        }
-    }
 }
 
 #[derive(Debug)]