That depends on whether you think that MWI is making claims beyond what QM claims, or if you think that MWI is just a restatement of QM from another perspective. If the latter then the falsifiability of MWI is exactly the same as the falsifiability of QM itself.

Unfalsifiable does not mean pseudoscientific. Plenty of things might be unfalsifiable for humans (e.g. humans lack the cognitive capacity to conceive of ways to falsify them), but then easily falsifiable for whatever comes after humans.