How can I emulate this wheel from the mowing unit of a ride-on mower?
My first thought would be to try and build this using 2x 32017 - Technic Liftarm 5 Thin and the following combination of a 1/2 bush and a tire (same tire you have on the wheel on the black part of your build, though the front tire might fit too).



If you use a 2L axle (in red!) this should look quite sleek. Not sure if the tire is going to be tall enough to support the mower, but it would definitely be sturdy, given that you're using Technic.