The new one should have come with a different adapter.

I Agree with Chispa, placing a semi-flush at the center of the powder room will give you a great amount of light. These are some good options. the warda semi-flush comes in four finishes and three sizes https://www.douniahome.com/collections/semi-flush-mount-ceiling-lights this is also a nice geometric option it comes in four finishes and three sizes https://www.douniahome.com/collections/semi-flush-mount-ceiling-lights/products/ula-semi-flush-mount-light

First, here's a "hi hat" light, like you might find in a school gymnasium: As it appears now, you are borrowing both the Foyer light and Hall light as your main sources of Living Room lighting (I do see a reading light over the chair though). If you'd like recessed (aka "can," or "pot") lighting for a general sustained illumination across the whole room instead of table/floor lamps, that is an option if you like that. You can leave the chandelier in the Foyer if you desire the decor function a chandelier gives at a "formal" guest entry. Just use it only when needed for circulation on the stair. Or, you can put recessed lights there instead. You can put a recessed light in the hall just for hall circulation if you want. In the hall you shouldn't have a problem fitting a remodel can, certainly a wafer light, in between the attic access panel and return grille.

It's not a simple answer. If keeping those locations and removing the fan, 6" would serve better for lighting, but I don't think you will be switching to 6" because: - if you have existing 4" new construction housings (Edison), it is too much trouble just to bump up to 6" integral LED fixtures as you are tearing out the ceiling to remove the housings. Really not even a reason to install 4" retrofit LED fixtures into the existing 4" new construction housings, unless you like the flush lens look. So if you are tearing out, go with a new layout and 4". - If you have existing 4" remodel housings or 4" integral LED's, then you can easily remove them and bump up to 6". But, in this scenario, because they are so easy to remove, adding in a couple more fixtures in between the existing would be easy too, which then should all be 4" fixtures. - If you are saying you will put a recessed light at the fan, I wouldn't. - The first assumption is they are 4" from estimating size from the pictures, and when lit you can't tell if they are old Edison trims or new integral LEDs. ______________ If this is swahili to you, look up about what the differences are between: - recessed new construction housings - recessed remodel housings - integral LED recessed lights - integral LED retrofit recessed lights