The syntax highlighting solution is provided by this TextMate Grammar, which is originally made for Atom, and also used in GitHub Linguist.
To enable Texinfo syntax highlighting when editing a file, it should be
recognized as a Texinfo document by Visual Studio Code. For file names with
suffix .texi, .txi or .texinfo, this process should be
automatic. If not, find and click the status bar item with “Select Language
Mode” tooltip, then choose “Texinfo” in the menu which just popped up.
If syntax highlighting does not look satisfactory, try another color theme where keyword/operator colors are distinct. Some good examples are Solarized Light/Dark, Monokai, etc.
For details about how to change language mode or select color theme, see the Visual Studio Code User Guide.