The thing that worked for me is
Fonts looks weird at Loki (and just in my user session!). How do I fix it?
But I got an error:
GLib-GIO-Message: 21:06:40.395: Using the 'memory' GSettings backend.
Your settings will not be saved or shared with other applications.
I solved it as described here https://blog.csdn.net/juwenkailaodi/article/details/86525841]
After searching around, stumbling upon Twitter Color Emoji (spoiler: doesn't work on Linux - only for Firefox: https://github.com/eosrei/twemoji-color-font/issues/10#issuecomment-242988370 )
...and a bit of stumbling around, I found the solution on reddit: How to better enable Color Emojis!
Here it goes!
Create a 75-noto-color-emoji.conf file ...