Wiring a bathroom fan light combo to replace light only

Hi, I need help with something that's probably really simple for someone who knows electrical, which I don't. I have a bathroom with no vent fan. Went to HD and bought a home netwerks ventilating bath fan, model 7130-02-bt. I thought I could simply swap it out with the existing light fixture and switch I'm using, but there's one minor difference and I'm lost.

Here's my original switch with the standard black, white, and green wiring. I've swapped out these switches before, but that's about it. https://ibb.co/k6UMRa

Then here's the new fan/light with black, white, green wiring that seems like will just be connected the same way the old light fixture was and is doable. https://ibb.co/mLy9CF

Now when I look at the new switch and want to start what I thought would be simple, there's an extra red wire on top of the black, white, and green. https://ibb.co/cNA6sF The wires are labeled and of course there's a wiring diagram in the manual https://ibb.co/bOzAKv

I know this seems like it would make things easy, but I'm not understanding it at all. I'm not getting how I swap out a standard, three wire switch with one that has four wires. I tried to google how to handle the extra red wire, but it seemed like the answer was that it replaces the black hot wire. If that is the case, that's still leaves the black then as an extra wire. I found one guy with the exact same thing as me on YouTube and tried to follow his wiring, but he had two original switches as one controlled the light and one the fan whereas I'm coming off of a single light switch. I don't know if that's the root of my problem and if so what I do about it. Anyway, I'm not following and if anybody has a simple explanation I'd really appreciate it.