Potentially a work around to get the rest would be downloading the SVGs from the tweemoji project and importing them into LightBurn, and perhaps then adding them to an Art Library for easy reference.
Could be related to ZWJ sequences or unicode version.
When I use code point, UTF-8, UTF-16, UTF-32, they look really similar. As an example:
Not working: U+1F310 - F0 9F 8C 90 - D83C DF10 - 0001F310
Working: U+1F4DA - F0 9F 93 9A - D83D DCDA - 0001F4DA