=()= is not an operator.

$scalar =()= EXPR
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is a funky way of writing

$scalar = ( () = EXPR )
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It consists of two operations: a list assignment (() = EXPR) as the RHS of a scalar assignment ($scalar = ...). Both types of assignments are documented in perlop, but the bits that apply are:

• The RHS of a list assignment is evaluated in list context.
• The RHS of a scalar assignment is evaluated in scalar context.
• A list assignment in scalar context returns the number of elements returned by its RHS.

In short, it's a means of evaluating an expression in list context and returning the number of elements returned instead of the elements themselves.

See Mini-Tutorial: Scalar vs List Assignment Operator