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.