Namely, I'm suggesting to add the icontains and iin keywords, the icount() function, and also the ilike keyword for completeness.
Maybe the names aren't ideal (in particular iin), but I don't think they are that bad, and they are consistent with the existing irlike (and the ircount() I'm suggesting in T334373).
Note the existing case-sensitive contains and in internally use the singlebyte strpos() PHP function, but for their case-insensitive counterparts we would have to use the multibyte mb_stripos() function, which would be significantly less performant (yet better than the current way of applying two lcase()). The point is that the case-insensitive variants should be used only when needed.
Related: T334373.