After upgrading my vcenter server to version 7.0.2 I discovered, that only very recent browsers are able to correctly display the webclient.
Initial page and login-page work on a variety of browsers. After you login successfully the issues start.
Internet explorer hangs with a spinnig wheel - and you can clear the browser cache several times - but that will not help;
the same experience I had with the old MS Edge browser, but it will boost CPU consumption to 100%;
also Firefox up to 68.11esr does not work - starting with 78.8.0 esr it does work - I don't know, which version inbetween is working;
all Chrome versions and Chrome-Edge seem to work .
That probably has to do with the fact that the webclient opens a multitude of browser sessions, despite the fact, that you habe only one screen/tab open.