There’s no practical tap limit!
The number that fit on screen is dynamic; it will depend on the number of features you have turned on (like whether or not to show a description), and of course the size of the screen.
When there are more taps than can fit, the display automatically separates them into multiple pages in a carousel, rotating between them.
You can simulate this by populating your taps, then go in to Look and Feel settings to play with the options. A real-time preview window will show you how it would appear on a 1920x1080 (tv-sized) display.