Yes, the Apple TV remote can turn ON your TV. When you connect an Apple TV 4K to your TV, in most cases, the Siri Remote will automatically turn ON/OFF your TV, control volume, and switch to the correct HDMI Input that your Apple TV 4K is connected to. You can press the Power button on the Siri Remote to turn ON your TV and Apple TV 4K. When you’re doing this, make sure the path between the remote and the front of your TV is clear. If anything blocks the IR sensor, you might not be able to turn ON the TV.
To turn everything OFF, just press and hold the Power button. Additionally, the volume controls would automatically work for speakers that you’ve selected, including the internal speakers or the external devices like a soundbar.
In case, the Apple TV doesn’t turn ON your TV automatically, you can configure the Siri Remote to do that for you. For this, open Settings on your Apple TV, select Remotes and Devices, and enable the Turn On the TV with your Remote option. Also, make sure that your TV supports HDMI-CEC and that it’s turned ON. In case you face any issues, please refer to the Apple support page.