The stacking style described below is well-matched to the height of the 3D printed keycaps. If you plan to use different keycaps, particularly low-profile keycaps, you should do a test fit of everything to check the height of the keycap vs the height of the screen. If you want a shorter screen height, there are lots of options you can explore with various ways of stacking short headers.
Solder male headers to the OLED
Insert male headers into the OLED from the bottom, then insert it into a solderless breadboard. Solder the male headers from the top side. Double check after soldering just one pad on each header that the headers are straight, not at an angle. Then, finish soldering the rest of the pads.
Solder stacking headers to the Feather
Insert the stacking headers into the Feather from the top, then insert the OLED into it. Solder the stacking headers from the bottom side. Double check after soldering just one pad on each header that the headers are straight, not at an angle. Then, finish soldering the rest of the pads.
If you're using short keycaps like the relegendable ones, here's one alternative way to stack it up. The short female headers go into the calculator PCB; the male headers' long ends are inserted into the bottom of the Feather microcontroller board and soldered from the top; and (standard) female headers are inserted from the bottom side of that PCB.
To get even shorter, you can desolder the STEMMA QT connector from the OLED and use short female headers on the OLED, or move the position of the microcontroller below the main PCB, which would require adding an opening in the main enclosure to access the USB connector.
These modifications probably also require modifications to the display bezel 3D print.