Well, I have never used Emoji directly on my Mac (M3). Because of this I have no idea when they disappeared.
However, I use Webex frequently and used emoji for reaction. Maybe this is another emoji I do not know...
But.
After upgrade to Sequoia emoji in Webex disappeared. I can't make any reaction nor insert smile into message. When I press Emoji and symbols there is no any reaction.
Ok. Maybe it is a bug in Webex. However, I tried to see Emoji in Sequoia, but failed.
I pressed Ctr+Cmd+Space, Fn+E or Edit-Emoji & Symbols from menu - no effect.
Oh, yes. There is an effect. The process is started. However, there is no any visible effect.

Of course, I restarted my Mac many times and upgraded it from 15.0 to 15.0.1 as well as upgraded Webex.
Is there any way to check if Emoji exists on my Mac?
Note, on my MacBook with the same versions of OS and Webex I can open emoji by Fn+E and from Webex.
So, something is wrong with iMac.