Support for GitHub Codespaces

Is your feature request related to a problem? Please describe.
Yes, It is related to a very big problem which most of the people may not realize that it exists. Let me explain what is that problem. I am from India and I teach web development on YouTube. Almost every student in India has mobile phone here but they do not have laptop since it is expensive for students. Most of them ask "Sir, Can we learn web development in mobile?" and I say used to say that "No, We don't have right tools to learn it on the mobile phone". But since GitHub Codespaces were launched I started telling that "Yes, we can learn web development in mobile". Now with the help of GitHub Codespaces we can use VS Code in mobile phone and with external keyboard and mouse it works very well and live server extension shows the output instantly. But in order to learn web development properly we need browser devtools and if this extension starts supporting GitHub Codespaces that will be game changer.

Describe the solution you'd like:
I want this extension to work on GitHub Codespaces exactly the way it works in the VS Code locally.

Describe alternatives you've considered:
For now my students use free tier of online testing platforms like Brower Stack, Lambda Test, and Sauce Labs only for accessing browser devtools. And their free tier is very limited (only few minutes) which is very frustrating.

Additional context:

Start by investigating how the extension connects to Microsoft Edge in local VS Code and what differs when running in GitHub Codespaces. The requested outcome is equivalent extension behavior in Codespaces, including browser DevTools access; the issue does not name specific files or tests to run.