Ehh, game engines are not really retained-mode in the way you mean. There isn't usually a cordoned-off piece of state that represents visuals only. Rather, much of that state is produced each frame from the mixture of state that serves all purposes (collision detection, game event logic, etc).
"What happens if you try to present an immediate mode API for UIs is the status quo with APIs like Skia-GL."
I don't know what Skia-GL is, but in games, the more experienced people tend to use immediate-mode for UIs. (This trend has a name, "IMGUI". I say 'more-experienced people' because less-experienced people will do it just by copying some API that already exists, and these tend to be retained-mode because that is how UIs are usually done). UIs are tremendously less painful when done as IMGUI, and they are also faster; at least, this is my experienced. [There is another case when people use retained-mode stuff, and that's when they are using some system where content people build a UI in Flash or something and they want to repro that in the game engine; thus the UI is fundamentally retained-mode in nature. I am not a super-big fan of this approach but it does happen.]
"and you draw strictly in back to front order so you completely lose your Z-buffer"
That sounds more like a limitation of the way the library is programmed than anything to do with retained or immediate mode. There may also be some confusion about causation here. (Keep in mind that Z buffers aren't useful in the regular way if translucency is happening, so if a UI system wants to support translucency in the general case, that alone is a reason why it might go painter's algorithm, regardless of whether it's retained or immediate).
"But that's the API that these '90s style UI libraries force you into."
90s-style UI libraries are stuff like Motif and Xlib and MFC ... all retained mode!
I don't agree that an IMGUI style forces you into any more shader switches than you already would have. It just requires you to be motivated to avoid shader switches. You could say that it mildly or moderately encourages you to have more shader switches, and I would not necessarily disagree. That said, UI rendering is usually such a light workload compared to general game rendering that we don't worry too much about its efficiency -- which is another reason why game people are so flabbergasted by the modern slowness of 2D applications, they are doing almost no work in principle.
Back to the retained versus IMGUI point ... If anything, there is great potential for the retained mode version to be slower, since it will usually be navigating a tree of cache-unfriendly heap-allocated nodes many times in order to draw stuff, whereas the IMGUI version is generating data as needed so it is much easier to avoid such CPU-bottlenecking operations.