It doesn't sound like you know what you're talking about. It being unfalsifiable doesn't mean that it is debunked. It just means that it cannot be empirically proven over other competing interpretations, which also are probably unfalsifiable as well.

I actually don't favor many worlds interpretation, but that does not preclude it as there's no way to test and verify any model currently.

Additionally there are also other models of how a multiverse would exist. If the universe goes on for infinite, or if there are multiple bubble universes with own big bang/creation event which would give the same affect. All unfalsifiable btw because it extends outside the scope of any measurement that we can ever make.