You’ve described my past frenchie to a T.
he always ate and drank a ton but couldn’t keep weight on him. He was 5kg for years, and then dropped to 3.8kg. It was horrible. He was diagnosed with EC which I’m sure absolutely wrecked havoc on his kidneys, because he also was incontinent. He never made it to his recheck to see how much his kidneys were actually impacted by it, but it was evident by his symptoms (excess thirst, hunger, inability to gain weight) that it had done something. He was like that for close to a year.
Not to concern you, but I’d definitely run a blood test. If it’s not EC, I agree with the other suggestion of it also possibly being megacolon – that “pot belly” appearance you’ve described (skinny on top but with a pudgy tummy) is a symptom of rabbits with megacolon. I wouldn’t let your vet shrug you off! I’d discuss these options with them and go from there. But based on what you’ve described, I’d say there is definitely something going on with your bun that is not normal.
also for what it’s worth: my rabbits have always gone to the vet annually for check ups. Both of them had mouth exams recently and vet saw nothing wrong. Then when they both had CT scans, we discovered they both actually had dental disease – so wouldn’t rule out possible dental issue either, though I do think megacolon is your most likely culprit here