So im playing on a modpack called permafrost eyes of the storm and when i burned the pillager banners, it didnt give me the bad omen effect even though in a video i watched about this modpack, he got bad omen.

how does this relate to eidolon?

Dont know i just assumed it was related to eidolon cause when you burn it theres the burning animation that looks like when you do the rituals in eidolon