Looks like it's officially possible to self-host vscode server and access it through vscode.dev (also see this GitHub issue).
For reaching it through custom URL consider using Gitpod's OpenVSCode Server fork of vscode.
If you just want to share your configuration between machines, it's probably simplest to just use settings sync, which is available in default installation.
Answer from Matija Sirk on Stack OverflowGoal
Having multiple containers with different vscode instances.
Example: I want one container with a vscode with the necessary extensions (and dependecies) to do web development, other container to do back-end development, and other to do data-science development. This will avoid having tons of extensions in the same VScode instance, wich sometimes, causes conflicts.
As far as i know, this can be done accessing via browser pointing to a port of the container running VScode right? Can i access without the need of browser? This is because i use a lot keyshortcuts and i'm afraid they don't work if use VScode via browser. Also, is the performance a concern or will it run smoothly?
Some references
site A
site B
If you have other references other than the ones i provided, please share.
How to use docker desktop for Windows with VS Code
visual studio code - open a file in docker container with vscode - Stack Overflow
How to use Dev Containers in VSCode without Docker Desktop?
Installing VS Code in a Docker container
Videos
With the May, 2nd 2019 announcement of "Remote Development with VS Code", you actually can use The Remote - Containers extension :

The Remote - Containers extension lets you use a Docker container as a full-featured development environment.
Containers make a great development environment because you can:
- Develop with a consistent and easily reproducible toolchain and on the same operating system you are deploying to.
- Quickly swap between different, isolated development environments and safely make updates without worrying about impacting your local machine.
- Make it easy for new team members / contributors to get up and running in a consistent development environment.
Docker extension for VS Code (ms-azuretools.vscode-docker) allows you to right-click on any running container in the list, then choose 'Attach Visual Studio Code' - and you will be able to open any folder inside Docker container in a new VS Code window. I presume you must have The Remote - Containers extensions installed as well.
Hello,
I have been using VS Code for some years and recently started using Docker, but I am not an expert in IT infrastructure so I would like to know if it is possible to literally have VS Code and the elements required to use notebooks (Ipykernel, Python, etc) installed in a container, so that I can directly use it anywhere.
The reason for this approach is that I am working with some data hosted in an offline server, and the only way to work in there is through the packages and modules you install in a container. I can already use Jupyter notebook as it seems to be quite simple to get - just including python, its packages, and Jupyter notebook in the container.
However, I really am not a fan of Jupyter and I would love to set up a way to have VS Code run on that server. I would greatly appreciate any tips that anyone could give :)
Thanks a lot!
Best regards,
Red muffin