As much as we'd love to be able to support Omnibug in every browser on the market, unfortunately the required APIs for us to build and use Omnibug just don't exist for several browsers. Right now, Omnibug is only supported on Google's Chrome and Mozilla's Firefox. Microsoft Edge support will come if Microsoft enables the devtools.panels API. You can help us out by voting on this suggestion, and hopefully Microsoft will add it soon!
If there are other browsers you'd like for Omnibug to be added to, please reach out to us via our GitHub issues to make a suggestion!