Has your Dr done any bloods? We had the same and the blood tests showed low iron and potential coeliac. We’ve been referred to a gastroenterologist. He’s been on iron for 3 months, a probiotic and a week’s worth of antibiotics to rule out a parasite and things seem more solid.
One of my girls never had a solid poo when in nappies and I mean frequent poonarmies, seeing previous food eaten etc. we still managed to toilet train her and actually her poos are better she hasn't had a poo accident since 4 weeks potty trained (started in August) and they come out a very soft log. Give it a try he may surprise you but don't be surprised if you get poo accidents for 4-6 weeks. We had 1 or 2 in potty to start with then accidents for 4 weeks, the other twin 6 weeks.
It took our son ages to do ‘solid’ poos, like at least 2.5 years, I’d say now they somewhat solid but still soft, they come out log shaped but definitely on the softer side but he’s fully toilet trained now so it’s harder to tell. I should think if the doctor says all is well you should be fine and give pops on the potty or toilet a try! Will be a much easier clean up for you too!