There is nothing different between calling from a WebRTC client to a WebRTC client and calling from a desk phone to a desk phone. They both work the same way within Asterisk, so any documentation for that is applicable. You really just need to use Dial() in the dialplan to call the other client.
I haven’t used chan_sip for WebRTC in years so I can’t comment on specifics (someone else may be able to) but is the websocket connection from the browser to Asterisk still up when you attempt to call? That’s the only thing that comes to mind, otherwise there may be something else with your configuration (I haven’t seen any issue reports in recent times or anyone mention this).