Can my external monitor charge 16" MacBook Pro over USB-C while using it? I am planning to use my new 16" MacBook Pro with an external display which is equipped with a USB-C output. I use the setup generally in extended display mode, and sometimes in clamshell mode.

I am planning to use a single, USB-C 3.1 cable to both drive the display and keep the MacBook connected to power. I'll be actively using the machine while it's connected.

My questions is, since the new 16" MacBook is equipped with a larger battery (100-Wh), and comes with a denser power brick (96 Watt), will the output from the monitor be adequate to charge the MacBook? If it depends on the monitor type, how do I determine if the output would be adequate?
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.