I am looking for pendant lighting for over my vanity and a flushmount light to match for the ceiling

Hi Rishab, You can avoid creating 4" false ceiling and create 1.5 / 2" false ceilings just to let the wires hide and run within the false ceiling. I will not recommend conduits or exposee ceiling unless you wish to do a rustic interior design. You can go for Surface mounted lights and track lights. They are beautiful and are available in different shapes and sizes too.

pendant lights looks nice only if place above a table like a breakfast nook or island. hanging them freely does not complement their look. since there is no island under the ceiling try to embed recessed lights in the ceiling. alternatively track lights will also look great if you need brightness.

Greetings from Aura you have two options here go for indirect wall lights or wall lamps direct pendent lighting from slab point would also look good many ceiling lights options available suitable for no False Ceiling wall lights are always better it creates ambience.