I found when my last girl didn't feel good and wasn't eating I had to entice her with foraged yard greens and that got the appetite rolling.
Dandelion, plantin, lavender, blackberry leaves.. all good for pain and helping digestion and get the gut moving.
If that doesn't work try some romaine or herbs such as dill, parsley etc. Wiggle under buns nose so he'll bite at it instead if letting him decide to say no straight up
I have heard giving a lightly made chamomile tea is good for their tummy's too.
Keep a close eye on bun and keep us posted on the progress. Hopefully bun bun will be eating by now and using the bathroom. That is the most important part.
Sorry I'm late to the question.. always hard waiting for answers to help you through to make wise decisions.
Sadly my girl did pass when she was 4 1/2, broke my world . Never did find out what went wrong. All I know is it all happened in 8 days. From her "not being herself" to dying in my hand at the vet.. so know when to go, and good luck to you and bunbun.
P.s. if you are not sure about syringe feeding, I recommend taking bun to vet and bypassing that option because you can also do it wrong (too fast, too much food etc) and it can cause bunny to choke. (They can't vomit)