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.
- Introduce websearch end to complement the begin
- Moves the logic of adding the sebsearch tool to
create_tools_json_for_responses_api
- Making it the client responsibility to toggle the tool on or off
- Other misc in #2371 post commit feedback
- Show the query:
<img width="1392" height="151" alt="image"
src="https://github.com/user-attachments/assets/8457f1a6-f851-44cf-bcca-0d4fe460ce89"
/>