Rework of https://github.com/zed-industries/zed/pull/30783

Before:

<img width="483" alt="before_1"
src="https://github.com/user-attachments/assets/c08531ce-0c1c-4a91-8375-4542220fc1b1"
/>

<img width="250" alt="before_2"
src="https://github.com/user-attachments/assets/e6f5404e-4e00-4125-bf2b-59a5bc6c41c1"
/>

<img width="369" alt="before_3"
src="https://github.com/user-attachments/assets/6a17c63d-80f6-4d91-a63b-69a9d8fe533a"
/>

After:

<img width="443" alt="after_1"
src="https://github.com/user-attachments/assets/4f7203c2-0065-41da-b7df-02aeba89ab7b"
/>

<img width="246" alt="after_2"
src="https://github.com/user-attachments/assets/585e2e25-bf06-4cdc-bfa5-930e0405c8d0"
/>

<img width="371" alt="after_3"
src="https://github.com/user-attachments/assets/54585f1a-6a9b-45a3-9d77-b0bb1ace580b"
/>


Release Notes:

- Allowed running certain Zed actions when headless