It seems odd that you cannot control the temp to the new one

i would read through the owners manual on adjustment to make sure you did not miss something. That is not a reflection on you but rather controls getting smarter and companies making overly complex items now. Sometimes it takes reading through it several times to understand the verbiage.

But it could be just a bad electrical component too.

I sooner think there is a setting overide you might be missing though. PLC PLC,s are now overly complex.

I would call the installer and listen carefully to what they say. If they explain that this is "normal" ask them to repeat why and write it down and check.

The water heater itself is unlikely to be related to the problem. It's a tank that sits passively as a reservoir of heated water. Household water pressure feeds in (through a tube to) the bottom of the tank and pushes already-heated water out the top. Have your plumber investigate the water distribution path from the tank to the faucet(s) that are exhibiting the problem.

Check BOTH heating elements.

I called the manufacturer today and did some troubleshooting. It seems as if I have a cross-over due to a faulty washing machine mixing valve. So, a call to the plumber seems to be in order. Thank you all for your invaluable advice!