Warning: somewhat disgusting post!

Just got back from taking Teddy to the vet. Pretty stressful for him, bless.
She said he’s perfectly healthy (yay) and he got his vaccinations.
Been home about an hour and he started hopping around the room exploring for the first time, Luna freaked out a bit, but never mind. He did some normal poops and a couple of cecals, but I figured, stressful day, new house, new food, scary rabbit next door, etc. etc. 

Anyway, so he went back into his house and I noticed a drop of something on the floor, it looked like pee but didn’t smell. I followed a little trail of these drops to his house where I saw a mess in his litter box  I cleaned it all up which I realise I probably shouldn’t have now, haha. 
I fished a bit out of the bin and took a picture (lovely, I know)

Here what you can see is mostly normal but slightly squishy poops, as well as this sludgy stuff. It’s all a bit stuck together here but before I cleaned it up it almost looked like some squishy poop that then phased into this gelatinous pee coloured slime. (ew, sorry). 
There were a couple of spots of this slimy stuff that kind of looked like snot (do you Americans call it snot? boogers? mucus from nose?). This stuff was clear coloured. You can sort of see it in the picture, its the wet looking bit on the left.

I picked him up and had a look down below, and his butt looked sort of foamy.  Couldn’t tell if it was poop or pee in origin, but I’m guessing poop because it seemed sort of connected. 

I cleaned up and put him back in his litter box, and he seems fine. He’s stopped leaking/pooping/peeing or whatever it was and is now quite happy hopping about.  This whole thing lasted a minute or less.
Soooooo….
Is this diarrhea?
He’s stopped now – should I assume he’s okay? Obviously I’m keeping an eye on him.
I’m thinking it’s probably just stress; I’m in the process of gradually changing his food, it’s a new environment, and the vet must have been stressful. Is it possible it’s a reaction to the vaccination?