I’ve not had this happen I’m my own rabbits (that I know of!), but the kidneys becoming enlarged can often be due to:

1) kidney stones or ureter stones. The stones interrupting the flow of urine so it builds up and causes kidney to swell (hydronephrosis).

2) inflammation due to possible bacterial infection.

Stones would normally show in xrays, but they can be missed. Another set or ultrasound imaging may detect them or show other changes to the tissues.

Sometimes, tissue can become fibrous like scar tissue and the organ not function as efficiently as it should. More likely in older rabbits.

I feel like I should mention the parasite/microspore E cuniculi as another possibility.
It is thought that many rabbits can carry it from an early age and it lies dormant (usually in the kidneys). It’s when a rabbit becomes debilitated due to other illness, or just aging that this can become active. The spores becoming active causing inflammation.

Sending some <<>> for your rabbit! Let us know what results come in.

Only just saw this post.

Excellent help from jerseygirl as always. Hard to say if was the toy, understand your thinking…BUT glad to hear he is improving!

(((Healing))) vibes to your bunny. Good luck!