I do not have the reputation to comment on any of the answers. But as of 2024, none of these methods work.

Windows recognizes that the ssh.bat file is not ssh.exe, with or without the echo (at least that is what I conclude from

The specified path "C:\Users\<user>\ssh.bat" is not a valid SSH binary
Checking ssh with ...

It works effortlessly with plink. I can, in the terminal, say plink user@hostname while I have a ticket in MIT Kerberos, and I can get in. But it just can't with the methods used for VSCode. It would be so nice if we could have the ability to, instead of ssh-ing into the remote through a native Windows SSH client, use Plink and get the same functionality as the Remote SSH extension gives us.

But I guess I'll be programming using the terminal now.

I would love to be told by someone that there is still a way out.