how do I watch apple tv on my MacBook pro after subscribing on my iPhone

On macOS Catalina 10.15 or later, you would have the TV app in which to view Apple TV+ content and iTunes Store video content.

On macOS Mojave 10.14 or earlier, you would need to view Apple TV+ content on the web at tv.apple.com, and iTunes Store video content in the iTunes application.

See if your Mac is compatible with macOS Catalina 10.15 or later. macOS Catalina technical Specifications - Apple

See if your Mac is compatible with macOS Big Sur 11. macOS Big Sur technical Specifications - Apple

Hmmm … assuming you’re running a relatively recent MacOS … it should be in there “somewhere” as it’s part of the OS.

Odd behavior indeed. 🤔

Maybe something in this article might help:

https://support.apple.com/en-au/guide/tvapp-mac/atve382f24c/mac

Just make sure that your MBP is logged-in w/ the same AppleID as your iPhone.

Then click the AppleTV icon.