Tankless water heater causes magnets (ceiling fans, induction oven) to hum while actively heating water

The problem is probably that the new unit uses solid-state control to vary the power delivered to the heating elements, which makes it more energy-efficient than the old-fashioned on/off control. Those solid-state controllers are notorious for introducing harmonic "noise" on the mains, and a 13 kW one could easily affect other circuits fed from the same main breaker panel. Resistive loads like heaters and incandescent lights aren't affected much, but loud humming from magnetic/inductive loads is textbook harmonic interference.

The first thing I'd try is complain to Rheem about excessive harmonic noise. An expensive brand-name water heater should have some built-in EMI (Electro-Magnetic Interference) filtering to minimize the effect. If it's making your induction stove sing, it's definitely "excessive" harmonics, and it might possibly even damage sensitive electronics plugged in elsewhere in the house. (That's not very likely, but is technically possible, and if needed it might make a useful line of argument to get Rheem motivated to take you seriously.)

The traditional way to eliminate harmonic interference (used with industrial VFD variable-frequency motor controllers, for example) is to connect the "noisy load" (your water heater) via a harmonic filter or isolation transformer. That's very effective, but I can't say I've ever seen a 13 kW harmonic isolation transformer marketed toward residential use... and the cost may be prohibitive. Industrial electrical suppliers and data-center power-supply companies are the obvious place to start looking if you go that route.