I think the conflation is mostly from a confusion in terms. Old Sanskrit treatises and sketches on hand to hand combat somewhat resemble the techniques in Muay Boran, the ancient precursor to sport Muay Thai, more than Patanjali's yoga sutras that form the basis of what we today think of as "yoga."

But the term "yoga" was historically applied to many sorts of disciplines, both mental and physical. It is likely that Patanjali's sutras were largely general knowledge in ancient India as ways to stay fit and limber, basically like the calisthenics everyone does today.

So it's likely it would have been integrated as part of any physical training regimens that came out of India. So basically, the yoga techniques and postures would be part of the martial arts training in the same way push ups and jumping jacks are.