Cox's vendor broke the watchtv.cox.com website a while back with some updates that contained errors. As far as I know, Cox still has an open ticket for it, but issues won't be fixed until the vendor releases another update. Hopefully, the next update will fix the errors.
Try holding down the tab key until you see it pass thru "Full Screen" in the upper right of the screen. Then press the letter "M". The tab thing is a workaround to enable keyboard shortcuts to work. Pressing "M" toggles mute on/off. It may or may not help you, but the website has issues that were originally reported 7/16/2021 that haven't been fixed yet.