Can my external monitor charge 16" MacBook Pro over USB-C while using it?
It depends entirely on the monitor type. Some monitors support power delivery, some do not. You'll obviously want one that does support power delivery.

Next comes the rated power - it differs from monitor to monitor how many watts of power they can delivery over the cable. The size of the battery in the laptop doesn't matter here - the only thing that matters is that the monitor can deliver more watts than the laptop uses on average while connected. If it can deliver more, those watts are used to keep the battery charged. Ofcourse - the larger the difference (up to a point), the faster the charging will happen.

How many watts your laptop is using on average depend on your usage. I.e. if you run it almost idle, only checking mail a few times per day - it won't use much. If you're running complex 3D renders all the time - you'll use a lot.

If your monitor supports power delivery with a wattage around the 96W that the included power brick gives - then you should be OK. Note that the standard currently has a limit of 100W, so you can never go above that. For most people 85W is plenty, and for many less can also be good enough.