Assistant's history with screenshots is long and fraught with complications. First, Now on Tap added a screenshot option, then it was removed and re-added when it was renamed to Screen Search, and when the Assistant came, the screenshot option was nowhere to be found but it was added again through Assistant's What's on my screen feature. But it looks like Google has made it even easier to take a screenshot and it no longer requires special know-how.
Simply say or type, "take a screenshot," in Google Assistant, and the nice lady will reply with, "OK, taking a screenshot, touch to continue." The screenshot will appear in the background and the sharing menu will automatically show on top of it. This is better than before in that you don't need to manually tap to share, you don't need to do a screen search first and scroll to get the option, and you can do it on your homescreen (the previous implementation in Assistant didn't work on homescreens).
And just like previous iterations, screenshots taken with Assistant will clean up the notification bar and the navigation bar of buttons. Here's a sample from my Galaxy S7 Edge (no nav bar, so you can't see the effect there, but check the notification bar.)
Assistant screenshot (left) vs regular screenshot (right).