I don't know if medium cages exist. I use the short type with larger cogs.
I don't see why a smaller chain ring would make any difference to the functioning of the chain tensioner.
The long cage on a birdie is to keep the chain tension in folding to stop it coming off when folding. I changed to a short cage to get more ground clearance. This reduces the amount of sticks caught in the toggle gogs, I bought the large cogged rear mech so the chain turn was wider to reduce jamming. Seems to have worked well. Shimano Alturus mech.