New water heater installed about a week ago and water temp gets cold extremely fast!

Plumber returning, but wanted feedback:)

So, I checked the timing of when I started the hot water in my bathtub and within, about, three minutes the hot water felt lukewarm, then cold. About 15 to 20 minutes, it was hot, again.

I also checked the bathroom and kitchen sink. Also, and not always, both the hot and cold water pipes feel very warm to the touch.

So, I did research (google) and it seems it's most likely the temp setting vs the heating element.

My question: If it's a new water heater, does that make sense that the temp setting is so low for this to happen?

Thank you in advance!