The answer for your stated problem is that you need FTPS
and not SFTP
to support JES extensions for job submission and retrieval (as well as other z/OS specific capabilities).
Here is an article that goes over the details of FTPS in c#. Its the same command sequence using the SITE
command as you used under FTP.
For a comparison of SFTP and FTPS here is some information.
Found this link about FTPS
setup on z/OS from Share. This should get you started. It seems more practical and applied than going to knowledge center and shows the various options and capabilities. The original author, Alfred B Christensen, is an IBMer. The material is from 2011 but is still mostly applicable today.
Here is a comparison of the technologies:

Here is some more background.
The issue is that ...sftp understands a set of commands subcommands similar to those of ftp. according to the linked IBM manual for SFTP. The sftp
server implementation provided by IBM does not have the full set of extensions provided by the FTP Server
There are other servers out there with associated clients that can provide the capability. I'm not endorsing this product but it seems to be popular from google searches I've done Tectia The default implementation of sftp server
from IBM does not support the same extensions that ftp
does.
If you're looking for a seamless transition and need transport security ftps
is a better option but likely requires configuration on the z/OS system if its not already enabled.
The issue is not simply the client, it is the capability of the sftp
implementation on z/OS as well.