Appeal ad infinitum.
You’re thinking more strategically than most - it’s as much about HOW than WHAT.
If they screwed up (or screw up in the future) this could all backfire, bigly. The “fruit of the poisonous tree” principle says that if the method by which evidence is obtained is tainted, then the evidence itself is too and cannot be used. So it’s possible that if this can be proven, everything they took could be declared off-limits in this or future actions. Not to say it will, or that it should have been done, but over-zealous searches can end up hurting the prosecutors rather than helping.
Can Cohen appeal now that a decision by the judge was made?