In this case I think multiverse is both. Testability and falsifiability are closely related. But its possible to make a testable statement that can't be falsified in most examples I can think of the test can't be exhaustive.

A theory can be untestable but also falsifiable. For example, while the multiverse theory/interpretation may be untestable, it could be immediately falsified if QM were falsified.

Popper's falsifiability criterion was more aimed at theories like Marxism, where it seemed that within the theory there was always something available to account for an exception or challenge.