On top of Lv 20 being no badges, it's this:
source: https://www.gfinityesports.com/article/2528/pokemon-sword-and-shield-how-do-i-catch-very-strong-looking-pokemon
Also note, for your own raid (you are the host), if your badge count (level can be caught) is lower than the level of the mon you encounter (before it is reduced),
that encounter is shiny locked.