Calling out leople who trust software from ByteDance, and not calling out people who trust software by Microsoft (i.e. VSCode) is a bit hypocritic. Both are faceless corps that produce unethical software.
I'm always surprised when corporate IT departments allow that given what's not allowed these days.
The server installed on the remote machine is part of vscode itself called the REH (remote extension host). It’s the core of the editor running in headless mode on the server.
Here is an example open source implementation of the non-free binary client (it’s a 4 files that call various editor APIs) https://github.com/xaberus/vscode-remote-oss
This is REH entry (the binary installed on the remote machine) https://github.com/microsoft/vscode/tree/main/src/vs/server/...