does anyone know if they make a perch that can stick to mirrors or windows and will also catch droppings? i know they make them for larger birds but what about budgie sized?

You can buy shower perches which stick to tiles, glass, mirrors, etc. They usually come in sizes from small to large, so i'm sure you could find one budgie sized. :fear

i have seen those but i was looking for one that will catch poop and other mess

Maybe just put a piece of newspaper or paper towel under the perch. Budgie poo is so tiny and easy to clean up i wouldn't think there's a market for small poop-catching perches. :fear