I'm wondering if it's really too soft. All the peanut butter I've seen has been soft but stiff. I make "curls" with it on the bread. Soft is OK when the stool still has a shape.
Even if it doesn't hold a shape it can be normal. All of us are different. I had actual diarrhea for many years. I was diagnosed with irritable bowel syndrome. The treatment was to increase fiber and reduce stress. At least at that time there was no pill or medical treatment to make it go away.
With IBS one can have fully formed, soft but not diarrhea, and hard stools. One can go from "normal" to constipation to diarrhea. Irregularity can be part of it. The fact that his movements arenearly the same from day to day would indicate to me that it's probably not IBS.
I have heard of children having IBS but not toddlers. Even if it were IBS the treatment is in the diet. Plenty of fiber and avoid foods to which one is allergic. Some of us have more sensitive guts than others. I'd try increasing the fiber and eliminating foods to which he may be sensitive. If you want to try eliminating milk, use rice rather than soy milk. Soy is also a common allergen.
The BRAT diet is for diarrhea, no matter it's cause. It has the possibility of working even tho his stools have had this consistency all of his life because it has fiber and substances to make the stool more firm..
But, again, is it really diarrhea, or just a soft stool? Increasing fiber could make it firmer if that is needed. If he's healthy and feeling good I tend to think it's normal for him. If it were abnormal he'd have other symptoms.
If he's lactose intolerant, he'll have gas and abdominal pain. It it's food allergies he'd most likely also have an upset stomach and perhaps hives and/or itchy skin.
Also, 2, is young for poop related potty training. Don't expect him to get his poop in the toilet. If you're with him and his poop misses, you could try a toddler potty chair. His bottom will cover the hole and the poop will land inside. If he's knowing he needs to poop and makes a run for it, that is a different matter but I doubt that he's doing that at 2.