You are correct. Here's the answer:
“I couldn’t care less” vs. “I could care less”
These phrases, meant to communicate that someone doesn’t care about something, are often used interchangeably, even though only one of them technically conveys the intended meaning.
“I couldn’t care less” is the correct way to express having complete apathy toward something. When someone says, “I could care less,” they’re actually saying that they do care because there are other things they care less about. Usually, when someone says “I could care less,” they are actually trying to say the opposite.
Source: https://www.grammarly.com/blog/commonly-confused-words/couldnt-care-less/
Pretty much the same with "could of / should of / would of" which should actually be "could have / would have / should have" or in the short form "would've / should've / could've" and many people on AN keep saying/writing it wrong.