I think UI is the most important. The umbrella of UI contains every visual element that is not physically within the gameworld and without a good interface that meshes well with the game it will feel incomplete. Sound can be incredibly important, but a game can work without sound. Same for cutscenes. But UI needs to, at the very least, be responsive and functional for a proper game to be playable. For my UI to be immersive, I have made the screens representative of the game and its levels with colour coding and pause screen screenshot that is from the actual game. These make the menu feel like a transition into the game rather than screens separate from it.
:3< Storing widgets in the Player Controller allow them to be accessed at any time in any level with any character instead of necessitating the duplication of the code over and over again. It also allows for easy, universal changes instead of having to go through all instances making those changes again and again. When moving to another level, I want players to feel that they are being transported to that level through some in-game means, even if nonsensical teleportation. If it weren't as it was, they would feel like they are being taken out and put back in instead, which is immersion breaking.
I think the most important thing I learned about widgets and their connection to the other factors of a game's design is this: having everything in one place is incredibly important for scalability. It also helps keep track of what is where by implementing a system in which certain things are always in one place. Adding a background image helps give the player an idea of what they are going to play and can sometimes suggest game mechanics. Visual style of a menu can tell a player how well made a game is as well, because the style of the UI and the game are usually synced.
I think the most useful thing I learned is the value of a menu's synergy with the rest of the game on the coding side; the menu must be in its own area so that it can extend from that area and reach out to all other facets of the game. If it gets tangled, it will get lost in everything else, consequently making it incredibly hard to make usable.