There's passport control to exit and they're pretty good on catching Israelis. You won't be able to use a US passport to leave if you didn't enter on that passport. Granted, at that point they may not care about Covid rules, but we don't know that.
dont know how they set it up, but its very possible that by passport control u can show ur israeli passport, and wherever they check ur permissions to fly u show ur foreign passport.
things work like that over here