When & why did the word "muff" become a crass euphemism for a woman's crotch area?

Circa 1699 per OED. Figurative extension of the existing meaning.

https://grammarphobia.com/blog/2017/03/muff.html

a cozy fluffy tube

I think that's your why. As to when, no idea. I first heard people talk about "eating muff" or "muff diving" going back at least 25 years, but I'm sure it's probably much older than that.

I thought it came from the thing you have pictured. But for penis instead of hands. 🤷‍♂️

I remember it being common by the late '70s.

I use ear muffs to protect my ears from cold

edit: and in places it is popular to eat muffaletta