Tap water isn't recommended for drinking anywhere in Egypt, cruise ships included — this is standard, well-established travel guidance rather than anything specific to the Nile. Bottled water is the norm, and most cruise ships provide it freely in cabins and during meals as a standard part of the package.
What about brushing teeth and ice?
Brushing teeth with tap water is generally considered fine by most travelers, though some prefer bottled water for that too. Ice in drinks on organized tours and reputable ships is normally made from purified water, but asking is reasonable if you're ever unsure.
A reusable bottle, refilled from the ship's larger water dispensers where available, cuts down on single-use plastic over the length of the trip.
See What Food Is Served on a Nile Cruise? for the rest of what's typically included at meals.