At the moment, you can use the MSFS devkit from @dga711, which gives you the ability to refresh instruments as well as gives the ability to read the console log.
It has been available since roughly the release of the sim. You can find it here: GitHub - dga711/msfs-webui-devkit: This devkit is a mod and guidance for easier development of WebUI (Panels, MFD..) in Microsoft Flightsimulator 2020.
If you are developing a JS instrument and want to do it yourself instead of using the devkit, the standard window.reload() works just fine, just as you would in any other browser environment.
-Matt