Transparent proxy for SSH connection with VS Code in use

Question

As the title said, I'm looking for a method to use SSH via a http/socks5 proxy. The proxy service provider software is ClashForWindows.

Some notations

• C is a Windows 11 Home device running VS Code, with remote-SSH extension installed and enabled.
• S1, S2 are the remote servers, which is located in a lab under an intranet network. S1 is a web server on Arduino. S2 is a server with Windows 10 Server installed. Though the lab has its own public IPv4 address, it is blocked by the admin, which means I could not reach it by means of the public address.
• P is the proxy server.

Current situation

On C, ClashForWindows is installed and the proxy is enabled on 127.0.0.1:7890. Both http and socks5 are available since I'm using them on Edge browser with SwitchyOmega add-on.

To give an example of current situation, let's say S1 has an IP 10.0.0.7 and S2 has an IP 10.0.0.8.

Currently, I could use the browser on C to visit the website deployed on S1 through the proxy server. That is to say, C <--> P <--> S1 is working properly.

However, I cannot use the VS Code on C to establish SSH connection with S2, even though I have set proxy in VS Code settings. I've also tried to enable system proxy in settings of ClashForWindows. Details of proxy settings in VS Code can be seen in the picture below.

Problems to solve

1. How to achieve something like C <--> P <--> S2 ?
2. Are there any barriers for SSH connections to use a http/socks5 proxy ?