> There's no need to persist any object or structure because
This isn't quite correct, at least for the library internals. Dear ImGui does persist UI state between frames, the "immediate mode" term only describes how the API looks like to the user, not how the library behind the API is implemented. The user code doesn't need to keep "widget handles" around, and there is no "event handler code" that is called asynchronously. From the user's point of view, control flow is entirely sequential, the UI is described and input events are processed in the same linear control flow context. But this is just what the library user sees, what happens under the hood is very different (e.g. the internal UI state is not rebuilt every frame from scratch, instead the API calls cause changes to the internal UI representation, those API calls just happen to also contain all the information needed to create the required internal UI state if it doesn't exist yet).
There's also nothing preventing the library from only redrawing what has changed, it just turned out that redrawing everything is usually so fast that only drawing what has changed would just add complexity to the implementation for very little gain (even complex ImGui UIs are usually a few dozen drawcalls at most and don't take up any significant chunk of the per-frame budget).
This description may be simplified and in details also slightly incorrect, but it's important to point out that "immediate mode" only applies to the API, not to the implementation, because this argument is often brought up by critics (who often don't quite understand what the "immediate" in "immediate mode UIs" is actually about) as a reason why immediate mode UIs can never be as efficient as traditional "retained mode" UIs (in reality they usually are more efficient than traditional UIs, and situations where traditional UIs are ahead can be optimized in immediate mode UIs just as well).