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/tui/src/chatwidget.rs

@@ -1010,6 +1010,7 @@ impl ChatWidget {
                 self.on_background_event(message)
             }
             EventMsg::StreamError(StreamErrorEvent { message }) => self.on_stream_error(message),
+            EventMsg::UserMessage(..) => {}
             EventMsg::ConversationHistory(ev) => {
                 // Forward to App so it can process backtrack flows.
                 self.app_event_tx