Then the first thing I'd try as a differential diagnostic is using another screen reader when trying to insert an emoji. That would rule in JAWS as a likely culprit if everything works fine with another screen reader, or rule it out as the likely culprit if the issue persists.
Differential diagnosis of root causes is a tedious process of elimination where you have to take out factors one by one and hope you hit upon something as the beginning steps.
For something like using another screen reader, that's easy and straightforward and it gives you a lot of information right off the bat.
Brian - Windows 10 Pro, 64-Bit, Version 2004, Build 19041