Actually, C2 is capped at 60 FPS rendered
That's not true actually - C2 games run at the refresh rate of the display, at least in modern browsers. Also even if on some platform the game is being capped at 60 FPS, it's not C2 doing it, it's the browser engine - we've coded our engine to run at any refresh rate.
You generally can't get hardware information in a browser. Browser developers are very cagey about giving out hardware details since it improves fingerprinting on the web which has privacy implications. I don't think you actually need to get the refresh rate for what you described though - if you measure the FPS and the system is fast enough, then the FPS will report the refresh rate. You can default your graph to 60, but if the FPS goes over then set a new maximum for the graph. You could even round it up to known common refresh rates like 75, 120 etc.