For better or worse, thanks to emoji Zero Width Joiner support [1], we're well on our way to there being more than 4 billion potential Unicode "characters". 4 billion is only 32 bits and you start spending a few bits here on hair style and a few bits there on skin color and a few bits on "misc" and then allow arbitrary combinations of them into composite families [2] and you can burn through 32-bits fairly quickly.

I don't think we're there yet. I think if someone did make a complete list of "valid" emoji right now, which for the sake of argument I'll call "formally defined in the Unicode standard", it would even on an absolute scale look like we're a long ways away from a full 32-bits of valid combinations. But you have to think of this on the log scale because this is about "bits" and those four-person families are already quite a long ways along to a full 32 bits. It wouldn't take much more customization, or the formal addition of more people in a group, to get there.

And someone who knows more about Unicode than I do may be able to establish that there are already in the standard ways to get to more than 32 bits' worth of data in a single standardized glyph; I certainly wouldn't bet much against that already being true.

(Personally, I'll go with "worse". In hindsight, we should probably have frozen Unicode into the original Docomo (and the other phone company that had them) emoji necessary for interoperability, and then created the emoji as an extension into Unicode. It seems like it would be useful to "support Unicode" without having to come with the complete understanding of what is increasingly the most complicated "language" in Unicode; forget doing good Arabic rendering or trying to understand an ideographic language, the emojis blow all that complexity away now. But here we are.)

[1]: https://unicode.org/emoji/charts/emoji-zwj-sequences.html

[2]: https://www.unicode.org/reports/tr51/#Multi_Person_Groupings