I could not care less = there’s literally no more care left.
I could care less = the care meter is at ten (from hundred), so there a little bit care left.
I don’t use either one. I say “I don’t care.” And I don’t say it much.
I remember when “I could care less” came into common use, at least in my area (eastern Mass.). I was in high school. I had to ask the girl in front of me in homeroom what “I could care less” meant because it didn’t make any sense to me. I also disliked the snarky way it was usually spoken. So I didn’t pick it up at all.