Noticed in my game that while small roboports have a robot recharge rate, they do not actively charge robots while the large roboport does. Are small roboports not working correctly?

They use small roboports for charging. The point is that they are charged either when they are discharged, or after completing a task right before landing in roboport. Accordingly, if they charge on a medium or large roboport, it means that they charge after completing their task.

Yes I am aware that the small roboports are entirely for charging purposes however in my case I have a medium and a small roboport, the bots will all go to the medium to charge and not go to the small at all. If I just have a small roboport with no other roboport the bots seem to never go to it to charge and will just sit idle.

Maybe I am understanding this incorrectly but the bots if given only a small roboport to charge from will never go to it to charge.

I have noticed the same thing. The bots will only go to the medium and large one in my case. It is quite easy to notice because they crowd around the medium ones and the small ones are completely ignored.