Assistant’s home button shortcut on the Pixels is where you used to get Google Now on Tap, but that doesn’t really exist anymore as a standalone feature. The “Now” branding is completely absent from the settings, but the essence of Now on Tap continues to exist as part of Assistant on the Pixel.
Simply launch Assistant on any screen that isn’t the launcher and drag up. You’ll get cards for content found on the screen. It’s similar to Now on Tap, but Google just calls this screen search now. From there, you can use the contextual cards, or go on making Assistant commands.
You can also ask the Assistant contextual info based on what's on the screen. For example, when reading a website about Hawaii, you could simply summon the Assistant and ask "how's the weather there?" without even swiping up to get those screen search cards. The Assistant should give you the weather in Hawaii.