Usually it's discouraged to solve this kind of parsing with regex, but expecting that split could do this is even more than ambitious.

You would need look-arounds b/c both LHS and RHS could contain "operators".

Did you consider using something like SQL::Parser ?

Anyway the right approach¹ (IMHO) is to successively build a parse regex which starts from the left, by combining smaller parts like $clause = $lhs . $op . $rhs;

Like this you can also follow the official SQL grammar.

Saying this, there are already some BNF parsers available for Perl.

Good luck reinventing the wheel. ;-)

update

¹) not elaborating on the necessity to be able to recursively descent into nested structures like parens-groups and even sub-queries