Sending commands to semihosting in VSCode + cortex-debug
VSCode can do whatever the plugin you're using supports.  This isn't really a limitation of VSCode specifically.
Unfortunately, it IS a limitation of cortex-debug.  cortex-debug, as of this writing, does not support semihosting.  It doesn't work because it hasn't been added yet.  I would point you to the project's README.md on github under the planned features section:

I certainly understand the desire to move away from Eclipse.  But I don't think there is a solution here that won't involve either using a different VSCode plugin (if one exists), or perhaps exploring some other editors and see if they have any suitable plugins with semihosting support.
Or you could always try and add it yourself (and make a pull request if you do!) since it appears to already have most of the required functionality already there, so it might not be too difficult.  But I'm sure it isn't what you planned on spending your time on.
I know this wasn't the answer you wanted to hear, but that is the current situation.  On the plus, they do seem to at least be planning on adding it.