Hi again,
I tried to disable all the plugins and it still didn’t work. I also tried to remove Jetpack and re-add it again, didn’t work either.
I tried installing WordPress from scratch again and imported everything from my old site. Can confirm emojis works fine now so it must be something wrong with my old WordPress/Jetpack installation.
Thanks for the help!
I hit save without changing anything on WordPress permalink settings and it works now! Thank you very much.