By traditional, I mean the usual sort where you create the UI elements, you hold onto their state, and then render them based on their current state. As opposed to immediate mode GUIs where there is little state and your code determines what to draw and how to draw it every frame.

My current issue is with modifying UI elements based on game state. For example, you have a button tied to an object in the game. Depending on the object, that button might be disabled. Whether or not it should be disabled could change at any point. With an immediate mode GUI, it sounds very obvious how you would handle this, since you are already having your code evaluate the button to draw it. But in a traditional GUI where the button already exists and you have to actually put more effort into changing it, I'm curious how people handle this situation.

My current attempt is resulting in a lot of UI code being sprinkled throughout my game logic, changing UI states as game objects change, with lots of checks to see if the object changing is the one currently selected in the UI. This feels very messy, but I don't see an alternative without taking it to the immediate mode extreme.

Are there other ways of handling this more cleanly?

You can use some form of message passing or observers.

We use messages; a class can register to listen for specific messages from a specific game object, or for a specific message at the global level. We implemented this for core game logic, but it works equally well for UI or any kind of plugin that can act on or modify game state.

But isn't that essentially the same thing? Whether I litter my game code with sending messages, or with direct UI state changes, I'm still ending up with UI-specific code within the game logic.

The only way I can think of to keep UI updates out of the game logic is to go the IMGUI route and have the UI do its own checking of game state before drawing each component. But that ends up at the other extreme, where I'm implementing game logic twice, once for the game and once for the UI to check on the game. There has to be a middle ground.

Whether I litter my game code with sending messages, or with direct UI state changes, I'm still ending up with UI-specific code within the game logic.
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Messages aren't UI specific. When a player game object takes damage, it doesn't know or care about the UI. All it knows is it needs to send a "health changed" message.

UI code should hold references to the data it is displaying. That way, when the data changes, the UI changes also.

If the UI code caches values, so that you have to explicitly update it in order for the content to change, consider making the UI an observer of the data in question. When the data changes, all observers are notified that a change has taken place, and the UI will get this notification and read the latest value as a result.

I find this much preferable to immediate mode GUI programming - with IMGUIs it's easier to switch buttons off and on based on game state but the functionality is so limited. A regular GUI might have 5 or 10 different events that a simple control like a button or a text field might give out, such as focus changes, content changes, mouse over/out, mouse down/up/drag-in/drag-out... immediate mode just can't handle that in a reasonable way.