I mean this kindly, but with having had a baby recently, is there any PND at play here? I ask because OP's brusque, perfunctory tone, catastrophising about peoples' presumed response to an untrained 3yo, and self-judgement are traits common in posters with depression. If that is in the equation, it won't be helping.
Back to the main topic, OP you clearly are not being lazy and have clearly put in more effort than many other parents who claim to have toilet trained children by this age.
Have the break. Toilet training over winter is hard. It becomes easier in the warmer months when you can be outside more and use the washing line.
My DS1 was born at the same point in the school year. We tried in the summer when he was 2.5 and it just didn't compute. I had a new baby and struggled enough with movement to do anything about it prior to that. We had a break and started again at 3. We did get there, but it was a lot more work than with DS2 who critically was self-motivated at 2.5. That was no virtue on my part.
DS1 didn't get his autism or dyspraxia diagnosis for another 5+ years. We were aware of speech delays at the time though. He'd also had food allergies and intolerances that affected his digestive system for years.
Why do you think SNs could be a factor?
Pre-school will be helpful if they are because a group setting can be helpful for some of the development strategies. If EHCPs are required down the line, professional support helps. It's not an easy world to navigate and even tougher to get through in isolation.
I favoured going straight to pants and toilets just like grown-ups. It just made more sense going straight to the real thing than adding in fake transitions to retrain from again.
Take the break, change strategy and be kind to yourself about it. Some children are just more work than others. You have time on your side. He's about 41m old... you have 18 more months before yR starts. Hopefully that gives some context on what proportion of time on his life so far is at play. He will get there on time and you clearly are working at it.