Wattage of LED based growth light not consistent with LED usage
Only later did I realize that it said its a 2kW light, which seemed quite excessive as it is only the size of a small keyboard and not that densely populated with LEDs.

Low quality grow lights are advertised by their supposed incandescent equivalent wattage.  Usually if you look through the listing, they'll also give you the wall power.  However, lights like these usually use cheap, low efficiency diodes, so even with the wall power draw it is hard to know how much light you're getting.
Unless you only need to use the light briefly, it is usually a better idea to pay for higher efficiency LEDs.  If you do that, you'll get a specification for mols/s of photons per watt from which you can calculate the actual light output and thus size your light more accurately.  In the long run, high mol/j lighting is usually much cheaper unless you have very inexpensive electrical power.

So I did some digging and figured out that it is using 2835 model LEDs. I found a website where I can buy those &quot;by the meter&quot;. The website states that with 120 LEDs/meter it will use 24W/meter.

Watts per meter refers to strip lighting on a flexible substrate.  More likely you have a metal core PCB grow light, in which case you can have higher power per LED, so this isn't necessarily correct.