[DevTools] remove script tag immediately (#26233)

Fixes https://github.com/facebook/react/issues/25924 for React DevTools
specifically.

## Summary

If we remove the script after it's loaded, it creates a race condition
with other code. If some other code is searching for the first script
tag or first element of the document, this might broke it.

## How did you test this change?

I've tested in my local build that even if we remove the script tag
immediately, the code is still correctly executed.