My step sin was like that. He just didn't like to poop on the toilet he wouldn't even go in under ware he would pull pants down and squat in the floor ( it was disgusting) he was three. I noticed it was always a certain time of day so I'd watch him real carefully and noticed when he had to go put him on the toilet and maybe read together or something to relax him he also preferred to have a step stood under his feet so it felt like he was squattibg but on the potty. Maybe try to do something similar and if he doesn't go in the time your there say okay and just watch him and have him try again every 5 mins ( whatever time frame before he had a chance to go in his under ware) and I wouldn't do pull ups I'd do under ware and have him help clean them if he does mess in them. My other son is just turning one so I'm about to prepare for potty training in a few with him..
I am not sure that making a kid at age 3 clean his underwear is going to click for him in any way regarding holding poop. If my kid was pooping in something, I sure would rather have them be pullups than underpants. It's a bit surprising he is not pooping in the toilet at age 3, but not astonishing, some kids just take a bit longer. Is he frightened of the toilet?
There is a product like a stool under the feet except that it allows the person to squat a bit, called a "Squatty Potty" (I know there are others as well.) The theory is that there is a muscle that naturally stays shut at the anus and that squatting opens the muscle. An OK theory given that people evolved to squat and poop, not to sit on a chair and poop. You might give that a look-up and see if you think it will help.
We got toilet seats at Home Depot that have an inner ring that are smaller and an outer ring that is normal sized, and put them on our toilets. (They have a magnet so when you shut the lid, the littler ring nests up in the lid.) I think that using those calmed my son's fears of teetering on the toilet edge.
We also bought a video about potty training and it came with all sorts of gimmicks my son loved.
I think the biggest thing for my son, though, was being in a preschool where the teachers helped the kids use the toilets. The toilets were small and low, and in a bathroom with a window into the classroom, and if a kid needed assistance the teacher would help him with his clothes or whatever, and also the kids observed each other going in and out, in a very matter-of-fact way. Cannot remember if my son was still pooping in a diaper by then, but watching other kids who were having some difficulties with the transition get helped by the teachers, certainly cemented the lesson.