Quieter than your refrigerator, louder than a snoring mouse in the next room. The shower in the adjacent room will drown out the sound of the heater itself by a considerable margin.
The loudest they get is usually the flue-purge at the end of a burn when the blower runs full speed for a few seconds, at which point it might approach refrigerator levels if you're in the closet with it. I have a similar sized Takagi in the basement under my bathroom, adjacent to the master bedroom, with the vent 5' from the window, and in the bedroom I can't hear it running unless it's dead-quite in the house, with no water running in that bathroom, and even then I have to listen carefully. There's nothing separating me from the unit other than the subfloor & flooring, and what I hear most readily is the the faint sound of the flue purge cycle coming through the window.