Tramadol is an opioid. It can be given for pain, it’s bunny safe ccording to Medirabbit http://www.medirabbit.com/Safe_medication/Analgesics/safe_analgesics.htm
It’s more powerful than Metacam and less hard on the stomach lining. But as you are saying, it can cause gut slowdown. A vet has to weigh the pros and cons.
I found this. “Adequate analgesia is imperative, since rabbits are prey animals whose physiology has not evolved to withstand significant pain. Many practitioners have used NSAIDs successfully, but this is becoming more controversial in cases of ileus when other modes of analgesia are available. I prefer to use buprenorphine to ensure adequate analgesia, and will often send the rabbit home on Tramadol if discomfort is still present. Antibiotics for anaerobes may be indicated especially if significant gas is present, and over-the-counter simethicone may be given to increase comfort.”
Gastrointestinal tract stasis in rabbits | VETgirl Veterinary Continuing Education Blog
I know of one bunny that just recently had tramadol for bad tooth pain. It seemed to help him, Metacam was not enough to give him adequate pain relief. He wasn’t in stasis though, just empty because he couldn’t eat properly. He also had motility drugs and he did poop eventually, after having eaten properly. So that story is different.