If you're on Windows, windows key + period brings up the system-level emoji picker. Just thought I'd let you know in case you weren't aware there was even such a thing as a system-level emoji picker (I sure wasn't until someone on my team told me about it).
Unfortunately I’m on mac, but maybe I can just copy the emoji from a website and paste it. It didn’t occur to me it might get displayed correctly but not be selectable.