Codex clutters prompt field with Plan hint during unrelated prompt

What version of the IDE extension are you using?

0.4.76

What subscription do you have?

Plus

Which IDE are you using?

VSCode

What platform is your computer?

Windows 11 25H2

What issue are you seeing?

<img width="544" height="801" alt="Image" src="https://github.com/user-attachments/assets/6a069c10-ded6-43b6-9cf3-8b5500cf9df9" />

Codex will clutter prompt field with distracting hint that pops up any time the prompt contains word "Plan" regardless of if the user wants to use the planning mode or not. This is confusing and ruins train of thought.

What steps can reproduce the bug?

1. Have conversation with Codex about proposing changes to the code without Plan mode enabled.
2. Once Codex has proposed some changes, type something along the lines "Let's proceed with the Plan".

What is the expected behavior?

Codex UI doesn't bother users with flashing changes to the prompt field only because the prompt contains the word "Plan". There are many prompts that can contain the noun "Plan" with no intention of user to plan anything.

Additional information

If you really think the "Plan" feature needs better discoverability, just have it permanently present in the prompt box instead of nested under the + button, and show the keyboard shortcut when hovering over the Plan button. Current state that flickers into the existence and has permanent keyboard shortcut tooltip is hideous and distracting.