When you are casting your smartphone on a built-in tv, the TV is doing all the work (downloading and decoding the signal). Your phone is just a fancy remote control.
The Chromecast is downloading the video and sending it to the TV on the contrary.
An iPhone 14 Pro Max can play streamed video on the internal display for literally 25 hours on a single charge.
edit: the 14 Pro Max has a 17 Wh battery, which means it draws 0.7 W streaming and displaying video.
When you are casting your smartphone on a built-in tv, the TV is doing all the work (downloading and decoding the signal). Your phone is just a fancy remote control.
The Chromecast is downloading the video and sending it to the TV on the contrary.