Unfortunately, while you can pause and play a video on a Chromecast with a stock TV remote, you can’t do anything besides that. Even if your TV’s remote has other buttons like a home button or selection buttons, only the pause and play functions are supported. For finer control over your Chromecast, you’ll still need to use your phone or computer. The TV remote is mostly just for keeping within arm’s reach of the couch in case you need a quick pause.
This lack of functionality is on the Chromecast’s side rather than your TV’s. HDMI-CEC support is supposed to offer you complete control with whatever remote you’re using, but Chromecast only supports the pause and play commands for some reason. Maybe someday, Google will expand that support to include other essential functions like navigation, but until then, you’ll have to settle for the bare minimum.