The majority of GUI elements are based on the VIEW_W and VIEW_H macros, update those to match the desired screen size and a lot of things should "just work". (Battle elements and some misc stuff use the room size for positioning instead so make sure to update all "1x1 screen"-sized rooms like battle, evolution etc to match the new size). Also on overworld rooms, the viewport size + camera follow border size needs to be updated, since views are set up in the Room Editor instead of by code and they're all hardcoded to 640x360 / 320x180 right now.
You might need to make some sprites, fonts and other graphics elements bigger as well, since they might look weirdly tiny on a much larger screen (and you also change from a 16:9 to a 4:3 aspect ratio which might squish some things horizontally) but that's an optional UX thing and not something that's technically necessary for this to work.