Thanks for the responses. The instruction manual is not the greatest, but it does mention the following about electrical:
"The hood comes equipped with a 5 ft(1.5m) power cord with a NEMA 5-15 molded plug for connection to a 120 VAC, 60 Hz, 15 A Power outlet. This outlet must be located in the duct cover area above the hood.
...
If local codes permit, the power cord may be removed and the hood may be connected to a hard wired electrical connection."
I only see a couple small holes at the rear of the hood, and I don't think the existing jacketed wire can fit through. This is a long shot, but could I run the existing wire splice into the hood, and then setup the power outlet connection inside the hood? Ideally, I'd like to keep the plug intact.
For reference, here are some photos:

Overview

Duct Closeup - Builder used a circle to rectangular adapter, so I'll need more circular ducting.

Underneath View of Cabinet - Existing vent opening and wiring.

Old Hood Opening - The old hood actually had a punchout for a circular opening. I wonder why they went with the rectangular since that meant they needed to use an additional adapter.

New Hood Opening - The cable that you see is the power cord that comes up right by the opening. I'm pretty sure there's some work to be done with screwing things in place (that circular connection piece is loose inside the hood), but the instruction manual mentions nothing about this.

New Hood Rear - You can see one of the small holes where I was hoping to run wires through.

New Hood Stuff? - These came with the hood. The instructions didn't say anything about what to do with them.