On 2.0 stable, the HTML5 export has been substantially improved, but it can still be considered in a "beta" state.
Those browsers are known to be supported, in their recent versions:
There is an important caveat with Chrome though: unless you run it with --disable-web-security
command line option, it will refuse to load the HTML5 project on a file://
protocol because of security policies. The workaround is to host it on a Web server (which can be entirely static, so you can use literally any Web server) that you host on your own PC then access with http://localhost/
or on a remote Web server.
This may apply to Edge as well, but I haven't tested.
In any case, you should open the developer console (press F12) and look at potential JavaScript errors there.