Update extern-win.md

[sfshaza2]

Fixes #13175

Updates windows doc to explicitly state that the lifecycle process function snippet belongs in a custom external window's message handler.

[gemini-code-assist]

Code Review

This pull request updates the documentation for using external windows in Flutter Windows applications. The changes improve clarity by using a more descriptive example class name and refining the explanatory text. My review includes one suggestion to further clarify the relationship between a WndProc and a message handler method in the context of C++ Win32 programming, which could prevent confusion for developers.

[flutter-website-bot]

Visit the preview URL for this PR (updated for commit 4bb1ff0):

https://flutter-docs-prod--pr13179-fix-extern-win-clean-gvlw048y.web.app

[sfshaza2]

@loic-sharma, can you have the correct person review this?

[loic-sharma]

Looks good, thanks!

[loic-sharma]

@loic-sharma, can you have the correct person review this?

For Windows shenanigans, that'd be me or @mattkae from Canonical

[parlough]

The copy and formatting changes look good to me. Deferring to Loïc for the code changes and references.

Thanks!