Unfortunately you need the steam service for authentication, so steam cl won't work.
That said, all you need is a client. I think there should be already some third-party projects on this like the 3d cl.
But I have no idea how far those progressed and if they are a viable alternative.
That leaves you with the following options:
- Looking for an third-party cl
- Writing you own third-party cl with your class <- could be fun too
- Opening the official cl from the website and try to sideload your server instead of the official. (Proxy magic)
- Convincing the devs to release a docker with a hosted cl for educational purposes (staring at @artch )