How do you create a car part group?
Solution 1:
No sooner did I submit this question than I turned around and saw a tool in the shop that I'd not seen before since it was partially hidden behind a column. It's the "Spring Puller" and it's used to create and separate groups.
Once you select this item, you can select items to combine into a group. You just need to use the radial menu again and select to remove the part from the spring puller, then it appears in your inventory.
I'm going to leave the question up, since the tutorial wasn't very helpful in my opinion, and there doesn't seem to be a lot of documentation about this game that I could find useful.
Update: In the screenshot with the spring puller, on the right side is a tire machine too -- this is what is used, like the spring puller, to create "groups" of tires and rims. Side note: I found out that every time you attach a tire to a rim, it needs to be balanced in the machine next to that before you an attach it to the car.