I'm wondering if it's just me, but on all macOS versions in the last few years it's as if the emoji picker somehow ages. It works great for a few days after a reboot, but then only pops up but the selected emoji doesn't get inserted. It just gets ignored. Sometimes you can work around it for a while by launching the emoji picker not in something that accepts rich text but plain text only. Eventually it simply stops working until the next reboot. I've remapped its hotkey to be [Fn] if it matters.