Feature request: Solution for Code Editor

The current solution works for JupyterLab on Amazon SageMaker Studio. It would be great if a similar solution was developed for Code Editor too.

In general I haven't quite yet figured out how to access a server launched from within the Code Editor app via the browser similar to how you can do in Jupyter with `https://{id}.studio.{region}.sagemaker.aws/{jupyter|jupyterlab}/default/proxy/{port}`

Start by reading the repository's existing JupyterLab solution and then investigate how a server launched inside Amazon SageMaker Studio Code Editor can be reached through the browser. Confirm the supported Code Editor access pattern and define the expected equivalent behavior before estimating implementation work; the issue does not name files or tests.

Written by the indexing model from the issue text.