Interesting! I see there's a LaTeX highlighter but it seems there's no compiling add-on :(

You probably don't need a dedicated compiling add-on VS Code has a very simple, but capable, generic task running system. If you hit Ctrl+Shift+B ("Build" shortcut) it will launch and if it is the first time you've run it in that folder it will scaffold for you a sample JSON config file with a bunch of examples of how to configure it (and more examples are online).

Thanks! I tried the most basic building command possible and it works well. Displaying the PDF on the right panel would be very nice but it's a start. For reference I used the following tasks.json:

   {
    "version": "0.1.0",
    "command": "texify",
    "isShellCommand": true,
    "args": ["-p","${file}"],
    "isBuildCommand": true,
    "showOutput": "always"
   }