This is a diagram of space and time.
Radial distance increases from left to right
Time goes from bottom to top. The future timelike infinity is i+
As pointed out in the comments this already shows the evolution of the distribution of matter from past to future infinity. There is no need to use multiple diagrams.
That Penrose diagram does not represent an evaporating black hole it represents a collapsing star forming a black hole. And the matter of the black hole hitting the singularity (the horizontal r=0 line) There is no indication of Hawking radiation here.
It appers as if the blue area is changing in size and you are apparently trying to interpret it as growing and shrinking event horizon, but it is just the remnant of the stars matter. And it is shrinking the whole time! Do note that in this diagram constant size objects would look like a "lens" shape to begin with.
Penrose diagram is not very helpful for visualizing the evolution from schwarzschild spacetime to flat spacetime, because it does not really capture the curvature of space at all. The thing it represents is the possible causal future and past of certain events and it looks pretty much the same in both spacetimes, because it is flattened out in a way to keep lightcones straight diagonal lines. Think of it as a map of earth that is straightened so that latitude and longitude lines are straight. You no longer see the intrinsic curvature of the underlying space anymore.
For intuitive introduction of Penrose diagrams I recommend "Picturing Black holes" https://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/black_holes_picture/index.html
And more detailed discussion can be found at Leonard Susskind's Theoretical Minimum series: https://theoreticalminimum.com/courses/general-relativity/2012/fall