Keep Instant DevTools locked when opening error overlay (#94357)
### Why?
The Instant DevTools closes when opening the error overlay and continues
hydration. This is annoying when I wanted to check the error, but didn't
mean to stop the capture.
Before:
[github.com/user-attachments/assets/f1de72a9-5a2b-4e4e-bd7e-e7f36c975ea7](https://github.com/user-attachments/assets/f1de72a9-5a2b-4e4e-bd7e-e7f36c975ea7)
After:
https://github.com/user-attachments/assets/f060e11e-9d60-43f6-a1fd-ca735fad1aa1