I’m able to get actual fake fullscreen by using SDL_CreateWindow without fullscreen flags and the native resolution returned by SDL_GetDesktopDisplayMode. Don’t know how applicable this is to SDL_SetWindowResizable/SDL_SetWindowSize or whether or not it’s something that can be relied on to always work.
edit: Even with this method windows created with SDL_WINDOW_OPENGL appear to switch to regular fullscreen until focus is removed. While unfocused they switch to behaving like fake fullscreen windows (with a noticable screen blink when this happens). Windows that draw through a (direct3d) SDL_Renderer or SDL_GetWindowSurface will always act like fake fullscreen.
It’d be nice to have a flag that is unambiguously intended to be (and actually produces) fake fullscreen.