Is this the type of reasoning that could be used to basic math without errors (without using a dedicated math engine)? I wonder why that type of reasoning seems to struggle.

I think chatgpt is interesting in its ability to highlight the subtle variations in a concept we tend to think of as more of a single attribute (e.g. reasoning) because humans tend to do certain types of reasoning tasks at the same relative proficiency as others. No human can write complex code without being able to add large numbers, so they are often lumped into the same skill category.