Open the remote project as a folder. No SSH setup, no remote agent.
File, Open Folder, pick the project inside the shared folder. VS Code treats it as a local folder, because to the operating system it is one. Edits save back to the owning machine in under a second; a collaborator's saves appear when files are (re)opened, and VS Code offers its normal reload prompt when a file changes on disk.
Language servers and full-text search read many files. On the mount, those reads are on-demand fetches: the first index of a cold project pulls what it reads, then settles. On a fast link this is unremarkable; on a slow one, let the first index finish. Project-wide search after that runs against fetched content at local speed.
The integrated git works, with the same two rules as git anywhere on the mount: keep live_collab off on machines that run git (the default is off), and let one machine at a time run git operations in a working tree. The full reasoning is in Use git on a shared folder.