With your bun continuing to have consistent and ongoing oblong fecal droppings with no previous history of it prior to this past illness, it's a likely indication of acquired megacolon. It's caused by damage to the nerve cells that control the contractions of the digestive tract. This isn't the usual genetic form, but is acquired due to illness or surgical injury.
https://wabbitwiki.com/wiki/Megacolon
https://vgr1.com/megacolon/
Acquired megacolon can be a temporary condition (that can become permanent) caused by an irritant like a toxin, bacteria, or internal parasites like coccidia, or things like tumors or coronavirus. Or it can be a permanent condition if due to damage from abdominal surgery, or if a treatable condition goes untreated and it's severe enough to cause permanent damage.
www.medirabbit.com/EN/GI_diseases/Differential/mega_differential.htm
Coccidia was my first thought based on the runny poop and mucous you described, as these are typical indicators and would be the most common cause of these clinical signs in rabbits, as can the oblong poop be. The antibiotic needed is a different one than what your vet prescribed (if that was the only antibiotic your rabbit was given). And 3 months later it's very unlikely to be an active infection anymore, if this was the cause. Which would mean it caused permanent damage and why your bun continues to have the oblong fecal droppings.
From the article on megacolon:
"It's very important to check for other things like coccidia or dietary issues before going on to fully diagnose megacolon. However even these are frequently overlooked by vets and we've had some successes picking up missed coccidia and being able to recommend and suggest treatment for these bunnies, whose guts have then normalised and they've not been megacolon bunnies at all"
The only chance I can see that it isn't permanent and is still treatable, is if your bun has a different intestinal parasite like tapeworm, or if your bun still somehow has an active coccidia infection. Then there's a chance that with the correct treatment (which is praziquantel for tapeworms or a sulfa abx for coccidia) the symptoms could resolve.
Normally a fecal float test in the very least, would have been done initially, to determine if any parasites were the cause of your rabbits issues, especially to determine if it was from coccidia. It's my opinion that any good rabbit vet would have known to check this, so if your vet didn't, it might be a good idea to do some research and find a more knowledgeable rabbit vet to go to.
I'd suggest at this point, at a minimum, having a fecal float test done. You should be able to just take a sample in for testing, preferably 3 samples gathered over 3 days (and brought in for one fecal test) for the most accurate results, without needing to bring your rabbit in. However, if you really want to investigate if this might possibly still be treatable, you may need to also have xrays, ultrasound, and/or a blood test done. Though even with additional testing, the outcome may not change if permanent nerve damage occurred.
If this does end up being no longer treatable, you'll be dealing with megacolon type symptoms, so the managing of the condition is going to essentially be the same as it is with rabbits that have the genetic form of it. I've had 3 rabbits with megacolon over the years. One rabbit succumbed to it early in her life, but the other two, I was able to eventually manage it pretty well through the right diet. One of my rabbits was born with genetic megacolon. The other acquired it as a new rabbit to me, getting repeated bouts with stasis, though it is possible he had it genetically as well, as he was a 'Charlie' breed too.
Through some trial and error, I found the diet that worked best for them was a no pellet diet, with no high carb foods either. So no fruit, sugary foods, grains, starchy veg, even critical care which has added sugars and grains. Whenever I fed even the smallest amount of pellets (many varieties and brands were tried), one bun in particular would have even more irregularly shaped fecal poop that was sticky with mucous, and would have stomach discomfort and be prone to going into stasis.
Both buns were free fed medium coarse timothy hay, select leafy greens, select forage leaves, and a salt lick, and nothing else. The other bun had to have that particular semi coarse cut of hay, or he would get moist log shaped fecal droppings if the hay was too soft and leafy and not coarse enough. And too coarse would result in weight loss and nutrient deficiency. So I found the second cut with a mix of leaf and hard stems, worked the best to keep both buns fecal droppings as normal as was possible for them.
Their droppings would always be somewhat irregularly shaped, but this particular diet kept them as healthy as possible for a megacolon bun. And they were healthy and did really well for a few years, then one bun passed from a different illness (unknown asymptotic e. cuniculi) during his neuter surgery, and the other lived to be 5 (the normal life expectancy for a well managed case of megacolon) before a sudden decline and passing from the megacolon.
But every bun is different and what diet worked best for my rabbits might not be the best for yours. Anything new I tried, I started with very very small test amounts, then kept a close eye on changes in poop and for any signs of digestive discomfort. That would always give me an early indication that a food wasn't working before it could worsen into something more serious. That's why it's always important starting any new food one at a time and in small amounts. With the exception of grass hays, which are usually well tolerated with sudden introduction into the diet. Though some very soft rich cuts, fresh early growth grass, and grain hays may cause issues for some rabbits.
So that's what I would suspect is going on with your bun, how I would proceed, and what I know about managing this type of illness. It's a lot of info to take in and go over, but hopefully something in this will be helpful to you and your bun.