I don't remember installing a new version of NewPipe recently. But I guess I did (maybe late last night in a daze?), because today I've noticed a distinct UX improvement.
To get the URL for a video, I used to have to start a video, wait for it to load, tap on it to bring up a hidden set of tiny controls, and tap a share button. Not there's a big, easily identifiable 'Share' button (and an 'Open in browser' button), under the line of buttons that were already there under the video.