No fonts actually include emoji to any significant extent, and definitely not in colour.
Instead, OSes use a font fallback list where other fonts are substituted in for characters that are missing, and each OS provides one font that includes all the emoji as colour bitmaps.
There's various ways how to do those in fonts. I think Apple uses bitmaps. Microsoft uses several overlaid glyphs in different colors. And there's also a way of embedding SVG as glyphs in fonts.
Instead, OSes use a font fallback list where other fonts are substituted in for characters that are missing, and each OS provides one font that includes all the emoji as colour bitmaps.