When using a USB-C monitor with power delivery, does constantly having it plugged in damage the battery?
Solution 1:
No, having it constantly plugged in won't damage the battery.
The MacBook contains power management circuitry that ensures that the battery is not "overcharged".
So having a USB-C monitor that charges your MacBook plugged in at all times is no different from having an ordinary charger plugged in at all times.
Solution 2:
In short, no it will not damage your MacBook.
It's important to note that no matter how you charge your MacBook's battery (whether that be direct via USB C or through a secondary device such as a monitor), the MacBook will be still receiving the same amount of current. This ultimately means there is no difference, and it will still have to go through the Mac's overcharge-protection circuits.
Knowing this, we can safely say that before the power will reach the important internals, it would have gone through the proper circuitry to prevent overcharge.
In regards to how this circuitry works, it actually diverts the power from the battery if the Mac is on, or limits the current flow if the Mac is off.
You may have noticed that your MacBook gets warmer turned on connected to AC power - this is an unavoidable trait that occurs during charge. When your Mac is charging and turned on, it will be quite warm to the touch. However, you will notice that your MacBook will not be as warm when fully charged and plugged in, because the overcharge-protection is diverting the power directly to the Mac and not charging the battery. When the battery is fully charged your Mac will run directly off the AC power.
So, in conclusion, it's safe to assume that your MacBook will not be overcharged. However, it is always a good idea to disconnect the power delivery or turn off the power supply occasionally.