The Apple TV app on an Apple device will allow streaming using AirPlay, but does not support Chromecast (Google Cast). If your TV relies on Chromecast, then streaming over your home network of Apple TV+ content is not possible from iPhone to TV.
If you have a reasonably recent model smart TV, then it may support the Apple TV app directly on that TV.
If that is not supported, then you can consider an external HDMI-connected streaming device that supports the Apple TV app. That can be an Apple TV box, Roku, Fire TV, PlayStation (4, 5), Xbox (One, One S, X, S), ‘Chromecast with Google TV’-dongle, Nvidia Shield TV, or select TV provider boxes that support smart apps.
All the ways to watch Apple TV+ and more - Apple Support
Get the Apple TV app or Apple TV+ app on your smart TV or third party streaming device - Apple Support
Watch on these smart TVs and third party streaming devices - Apple Support
Lastly, with a proper HDMI adapter, you may connect your iPhone or Mac directly wired to a TV, to watch on the bigger screen that way. Not as convenient, but supported.