I doubt the credibility of the this claim but I believe the US do coordinate with both to make sure things do overlap.https://tribune.com.pk/story/1620736/6-israel-pakistans-enemy/
Is Israel Pakistan’s enemy?
Pakistan’s Israel policy historically has been driven by the position taken by the larger Muslim world against the Jewish state. But as a matter of fact proponents of that policy have now themselves embraced the change. Saudi Arabia is the prime example. It is an open secret that Saudi Arabia and Israel have been talking to each other for many years now to at least maintain some contacts if not establishing full diplomatic relations.