How to Case Apple TV+ to Chromecast?

Apple apps do not support Chromecast (now officially Google Cast).

Instead they support AirPlay, a somewhat similar but different protocol. Select TVs support AirPlay (list). Select streaming devices (Apple TV box, Roku) bring AirPlay support to connected TVs.

Well, in order to watch Apple TV Plus on your television you would either need a TV or external device that supports the app directly, or a TV that supports airplay (for casting from another device). If you don't meet those requirements, yes additional equipment would be needed. You can check the link below to verify.

Apple TV app - Devices - Apple (CA)

I don’t know what equipment you have …

What is your model smart TV? Possibly it is on the supported list for the Apple TV app (or Apple TV+ app).

Do you have any of these devices to connect to an unsupported TV? Fire TV, Nvidia Shield, Chromecast with Google TV dongle, PlayStation 4 or 5, Roku, Xbox One|One S|Series X|Series S? Those would also support the Apple TV app.

List of Apple TV app-supported smart TVs and third party streaming devices - Apple

All the ways to watch Apple TV+ - Apple Support