Replacing bathroom exhaust fan
Don't overcomplicate it. Sounds like you had a "fan and light" with wiring to be able to be switched separately, but actually wired so they were always switched together.

So, remove and insulate the red (what you call pink, but it's both commonly and clearly in your pictures: red) wire at both ends. Twisting on a small wirenut and taping that is a typical approach. You don't need it unless you want to have separately switched fan and light on a fixture that supports that, perhaps the next remodel.

Black to black, white to white, bare to green, call it a day.

Yes, you COULD leave the red and black together, but it's not actually right to do that if they are going to the same wire - fine when you had two separate wires at the fan, not fine without that.