Firefox/Gecko can also use Graphite for rendering (if the font supports Graphite), otherwise, yes, Harfbuzz would be used for the OpenType rendering.
While HarfBuzz can indeed be used on all operating systems, different applications may or may not use it. InDesign has it’s own OpenType shapper, older versions of LibreOffice used Uniscribe/DirectWrite on Windows, and something else on Linux. Now LibreOffice uses HarfBuzz everywhere. Microsoft Office would use DirectWritre, not HarfBuzz.
Older versions of Paratext used part of Internet Explorer (and thus Uniscribe) to render text, at one point Paratext on Windows could switch between IE/Uniscribe and Gecko/HarfBuzz.