I thought people would be more likely to find this here than buried in my abandoned Github repo. This example was developed on Ubuntu 23.10 and runs successfully on that platform with main branch SDL, incorporated as a submodule in the repo linked above.

#define SDL_MAIN_USE_CALLBACKS
#include <SDL3/SDL_main.h>
#include <SDL3/SDL_init.h>
#include <iostream>

namespace {
    /// The window we'll open to show our rendering inside.
    SDL_Window* window {nullptr};
}

extern "C" {

int SDL_AppInit(void **appstate, int argc, char **argv)
{
    std::cerr << "SDL_AppInit" << std::endl;

    int result = 0;
    if(result = SDL_InitSubSystem(SDL_INIT_VIDEO | SDL_INIT_EVENTS) < 0)
    {
        std::cerr << "SDL_InitSubSystem failed with code " << result << std::endl;
        goto error_exit;
    }
    SDL_SetEventEnabled(SDL_EVENT_TERMINATING, SDL_TRUE);
    SDL_SetEventEnabled(SDL_EVENT_DID_ENTER_BACKGROUND, SDL_TRUE);
    SDL_SetEventEnabled(SDL_EVENT_DID_ENTER_FOREGROUND, SDL_TRUE);
    SDL_SetEventEnabled(SDL_EVENT_KEY_DOWN, SDL_TRUE);
    SDL_SetEventEnabled(SDL_EVENT_KEY_UP, SDL_TRUE);
    SDL_SetEventEnabled(SDL_EVENT_MOUSE_MOTION, SDL_TRUE);

    window = SDL_CreateWindow( "SDL3 Window", 960, 540, 0 /* | SDL_WINDOW_VULKAN*/ );
    if( window == NULL )
    {
        std::cerr << "SDL_CreateWindow failed" << std::endl;
        goto error_exit;
    }

    return 0;

    error_exit:
    std::cerr << "Last SDL error: " << SDL_GetError() << std::endl;
    return -1;
}

int SDL_AppIterate(void *appstate)
{
    static thread_local int i = 0;
    ++i;
    return 0;
}

int SDL_AppEvent(void *appstate, const SDL_Event *event)
{
    std::cerr << "SDL_AppEvent";
    if(event)
    {
        std::cerr << ": type = " << event->type << ", timestamp = " << event->common.timestamp << std::endl;
    }
    std::cerr << std::endl;
    if(event->type == SDL_EVENT_QUIT)
    {
        std::cerr << "SDL_EVENT_QUIT" << std::endl;
        return 1;
    }
    return 0;
}

void SDL_AppQuit(void *appstate)
{
    std::cerr << "SDL_AppQuit" << std::endl;
    return;
}

}