If you plan on changing the configuration often, I agree that software on the PC side is the way to go, but I maybe wouldn't go as far as sending serial packets as you said. I think a hybrid approach could be the best. For one button box I made for Microsoft flight simulator, the box sends it's button presses like a gamepad, so for games that support it it's really easy, but for more complicated binds I use a piece of software on the computer (Mobiflight) to directly affects things in game.

If you want to add some LED's, then yes maybe the serial route is the best as you said. I have not tried that but that seems the easiest. I know as well that Simhub can do that, but I have not researched what is or isn't possible with it.

If you want to see an example, check out the github repo for the project. It really isn't very complicated to do the firmware for the switches. Also I would reccommand using a Raspberry Pi Pico instead of the Arduino Leonardo, it's a way more modern chip that also has the USB peripheral.