From what you describe- the first thing would be to treat it as if it were “urine scald” around her nails (though it sounds more like irritation than a true scald). Urine is a definite irritant. Since keeping the feet clean and dry would be recommended to ANY other diagnosis I would think this would be a good place to start. Meds can be tricky in that area as opposed to the back of the legs which often are bare when scalded. But all the fur around the toes which is likely contributing to the problem or keeping urine against the nail bed is what makes topical meds not ideal. I think a bunny would go nuts and insist on cleaning her feet.
Her toes should be cleaned to remove any lingering irritant, bacteria, etc that is present. Chlorhexadine or Betadine is a common cleaning antiseptic. (I am not familiar with Betadine- though I think that is the most common available to the public???) So using warm water- wet the back feet, use your fingers to get around the toes and to the irritated areas and apply the antiseptic wash, let sit at least briefly, and then follow with a warm water rinse. Because there is hair present – I would rinse to avoid the bunny ingesting any antiseptic. Then is will be important to make sure the bunnys feet stay warm and dry completely. (Maybe let her hop around the bathroom or laundry room with towels/rugs on the floor- as long as floor is not drafty). And while bunny’s feet are completely drying- her cage needs to be cleaned- especially the litterbox. And litterbox care will have to be diligent while the irritation is healing. Evaluate what litter is being used and if a different litter or more or less of same litter could keep her feet cleaner. And depending on the state of her litterbox- I think you would want to change it at LEAST daily- more often if her feet are still coming into contact with urine. If it helps- buy a second litterbox to swap in between cleanings.
I think this is a pretty safe route to follow- and even if the vet had seen enough of a problem to prescribe oral meds- it would still be important to keep the feet clean, free of irritants and dry. I suspect Sprinkles will be highly disapproving of the “toe bath” though- so prepare your ex for the stink eye and huge amounts of disapproval.
(Referenced book- When Your Rabbit Needs Special Care by Lucile Moore)- antiseptic wash was recommended- and I modified to what I would do for my own bunny with irritated nail beds and limitations of furry feet.