Or you could make life easy and get a 13mm OD standoff. They will have a partly drilled threaded hole in them that could easily be drilled through to 8MM. Many electronics places sell them, but here is a company that makes them as an illustration of what I mean. https://lyntron.com/catalog/LynTron/B12
I recently bought several couplers from Skycraft surplus, which is a great store here in Orlando, that were multiple sizes. However, I had no difficulty in drilling out one end or the other, or even both ends, to allow it to fit as needed.
Give them a shot, good selection, cheap and been around for a long time. https://www.skycraftsurplus.com/
I'm looking for ideas on how I could connect the following wheel, to the motor shaft below? Ideally, I would like to connect it directly, without a belt.
You may think that is a good idea but most motors have too much speed and not enough torque to directly drive a wheel that moves a car, a cart or whatever. Make sure your motor has enough torque for the job before you incest in the mechanical design effort.