I cleaned the engine bay using sonax engine cleaner followed by free running water from garden hose twice. Once on my 2012 Toyota Camry Hybrid XLE about a year ago and just 2 days ago on my 2019 Toyota Camry Hybrid XLE.
Each time I was careful to first wrap electrical parts with aluminum foil. I even sprayed a bit of WD40 before the foil wrap. And also the pulley, I read that you want to avoid water getting in to the bearing. So I wrap and tape the pulley area well.
After hosing it off, I used the leaf blower to dry it also. I didn't start car til the next day just to make sure all was really dried. I also used Sonus Trim & Motor Kote to dress it up.
Do this at your own risk. Safest thing to do is what you're been doing with damp cloth. Cheers.