Fix link to the JupyterLite example file in the documentation
Description
Follow-up to https://github.com/jupyterlab/jupyterlab-plugin-playground/pull/45
In https://github.com/jupyterlab/jupyterlab-plugin-playground/pull/45 it was noticed that the badge linking to the example file does not seem to be formatted correctly on ReadTheDocs:

Reproduce
This can be seen on the documentation website: https://jupyterlab-plugin-playground.readthedocs.io/en/latest/lite/lab
Expected behavior
It should be possible to click the badge and use the extension and open JupyterLite in a new tab.
Context
https://github.com/jupyterlab/jupyterlab-plugin-playground/pull/45
The badge in README does not seem to work right now either:
Will open a PR to update some jupyterlite dependencies to the latest versions to see if that can help already.