RemoteSSH: allow to detect or set remote PATH (user set PATH ignored)

Could it be possible to override the default SSHd given PATH on a remote, or better, have VSCode detect the user PATH when starting on a remote?

The use-case is:

• the user (non-admin) install more tools / newer tools on the remote host and want VSCode (+ extensions) to use them,
• so the user add entries to the PATH (using remote shell rc/profile files),
• however it seems VSCode doesn't start a login shell to detect the final user PATH and sticks with the SSHd given one, so only default PATH (system-wide) tools are available.

In a shell/terminal, user-installed tools are available however, since the rc/profile files are properly sourced here.

If I'm mistaken about this, and there's some PATH detection or some way to set a PATH for VSCode, could you explain how or point to a documentation?

Please note I searched for issues about this topic (is:issue in:title PATH label:ssh) and could not find anything like this request.

Start by tracing how the Remote-SSH extension starts VS Code on the remote host and obtains PATH; the issue contrasts the SSHd environment with shell rc/profile sourcing. Done means user-installed tools added through the remote user's PATH are available to VS Code and extensions, or the supported configuration is documented.