YouTube Shorts don’t have background play/PiP, at least not through the regular Shorts player. It is possible to get a Short pulled up through the main video player because each Short actually has a page you can access by just replacing /short/ with /v/ in the URL, and that will have background play and PiP if you have these enabled.
Tapping some URLs will inconsistently get you to the page too without having to do any URL replacement. I don’t think there’s any intended logic there, just some bugs in the way URLs get handled hopping from social media app to browser to social media app since most of them try to keep you silo’d in.