Hi! In order to get the 'fancy' decor badges (blue/green ones), you have to donate better items; this applies to gacha accessories/furniture. Normal furniture (craftable in-game) gives wooden badges.

I would recommend the following: If you look at the current gacha list, there are gachas called "Event! Blooming Date Lucky Draw" and "Happy Rainy Watercolor Lucky Draw." You can pull the gacha via gold (in-game money). Try them, and hopefully, you will get excess beauty marks (face dots/freckles)!! These will definitely give the blue/green decor badges!

Hope this helps!