Because a GitHub codespace runs inside of a Docker container (called a dev container), any feature of the MATLAB VS Code extension that requires an installation of MATLAB (like code execution) is not supported. You are still able to use basic features of the extension when editing .m files in VS Code, like syntax highlighting and code folding.
If you want to use MATLAB within a GitHub codespace, we do provide some reference architecture that uses MATLAB's Docker image. This involves modifying "devcontainer.json", the configuration file of the docker container that the GitHub codespace runs in. The instructions are detailed in this MathWorks repository on GitHub.
In order to open MATLAB within your browser inside of your GitHub codespace, we recommend following the instructions listed within the "Using the MATLAB Image on Docker Hub and MATLAB Proxy" section of the README. This link from the README should directly configure a codespace with the correct "devcontainer.json" file.
