Add the icon to the left side of the message editor, add a new icon for
when the thinking mode is toggled on, and add a keybinding for the
action. Currently available under a feature flag-only but should be out
soon.

<img width="400" height="318" alt="Screenshot 2026-01-29 at 11  57@2x"
src="https://github.com/user-attachments/assets/e033ec83-746b-4fed-beb7-ed26e96cb60a"
/>

Release Notes:

- N/A