I have been using Laptop computers (Windows and Mac) for the past 25 years and have used them while plugged in and charging around 95% of the time. I have never had to pay any attention to it and have not suffered any adverse effects. I learned that a battery will degrade in health over time no matter how I careful I am with it. In the end, I focused more on enjoying my expensive computer vs focusing on how I can squeeze a few more days out of the batteries life cycle.
You also mentioned that the base of your MacBook Pro gets hot. No part of your computer should ever get hot. Areas of your computer may get warn from time to time but should never get too hot to touch.
Axel F.