It wasn't obvious to me when I first started playing Wordle, but you can actually share an emoji-fied version of your game (without the letters) by clicking "Share" when the statistics window pops up. I didn't think to do that at first, but when I noticed everyone on social media posting their Wordles with the exact same format, I figured it had to be buried in the game somewhere.
The black and white squares are in the older Unicode "Miscellaneous Symbols and Arrrows" block so I guess they're allowed. Several things like that are sort of "retroactively" emoji... there's a "display as emoji" or "display as text" character you can put after them.
What HN does and doesn't allow seems somewhat arbitrary, things like the star emoji are in that same block and yet are not allowed as far as I can tell.