Waveshare 2.13 Inch e-Paper Display Hat(B) V3 and ESP-WROOM-32D

@declantiberius, Hi welcome to the world of e-paper displays!

Thank you for providing these pictures!

I don't have the same e-paper display from Waveshare.
I may ask them for a free sample, if it doesn't work with GxEPD2 yet. Or get one donated.

I assume your display is this one: 2.13inch E-Paper HAT (B), 250x122, Red/Black/White, SPI Interface.
Its wiki page is https://www.waveshare.com/wiki/2.13inch_e-Paper_HAT_(B).
From https://www.waveshare.com/wiki/2.13inch_e-Paper_HAT_(B)_Manual#Introduction:

V4: resolution of 250 × 122, V4 version hardware structure and interface compatible with V3 version, using V4 program. If you are buying for the first time and have a V4 label on the back of the screen, just use the V4 program.

The example from Waveshare with their driver code can be found here:
https://github.com/waveshareteam/e-Paper/tree/master/Arduino/epd2in13b_V4
Looking at epd2in13b_V4/epd2in13b_V4.cpp the controller might be SSD1680.

So there is a chance it might work as GDEY0213Z98. Try uncomment line 75:

//#define GxEPD2_DRIVER_CLASS GxEPD2_213_Z98c // GDEY0213Z98 122x250, SSD1680, (FPC-A002 20.04.08)

Don't forget to select the 3-color display class:

// select the display class (only one), matching the kind of display panel
#define GxEPD2_DISPLAY_CLASS GxEPD2_BW
//#define GxEPD2_DISPLAY_CLASS GxEPD2_3C
//#define GxEPD2_DISPLAY_CLASS GxEPD2_4C
//#define GxEPD2_DISPLAY_CLASS GxEPD2_7C

And make sure your wiring corresponds to the constructor parameters for your board.

If you still have a problem with your display, then report the inking you see on the flexible connector of the screen panel. And report all selections you made.

Good Luck!
-jz.