How Does Black Hole Evaporation Look From the Inside?
An infalling observer cannot remain stationary inside the event horizon of a black hole.

According to them, there is a short period of proper time before they meet whatever lies at the centre of the black hole (a singularity in GR).

If the observer looks back, they do not see an infinite amount of time pass by in the outside universe. In fact for the type of black hole where they might (a) survive and (b) have time to make any observations (i.e. a supermassive black hole) then they would see the outside universe only for a relatively short time longer than their experienced proper time and certainly for nowhere near as long as the Hawking radiation evaporation timescale. So the possibility that the black hole is (slowly) evaporating is of no consequence to their final moments.

The necessary material and diagrams to understand the previous paragraph have been covered before on both Physics and Astronomy SE.

https://physics.stackexchange.com/questions/82678/does-someone-falling-into-a-black-hole-see-the-end-of-the-universe

Would time go by infinitely fast when crossing the event horizon of a black hole?