I must admit that I am confused what works for you and what doesn't.
Here's the rundown.
I now have with slight modifications to the code the SPI based thermocouple reading program working on both systems. Modifications like /dev/spidev0.0 verses /dev/spi/0.0 and which GPIO pins are used since they are named differently. But all this works now!
The Pi does belong to the gpio group.
pi@raspberrypi:~/projects/lazarus/TC $ groups
pi adm dialout cdrom sudo audio video plugdev games users input netdev lpadmin gpio i2c spi
But still requires sudo to run the application as shown in the previous posting while the BBB now can debug from both inside and out of the IDE.
Here's the BBB accessing the thermocouple board.
debian@ebb:~/lazarus/TC$ ./TC
Reading temperature, press any key to exit...
Temperature: 21.5C 70.7F
Temperature: 21.5C 70.7F
I'm going to have to go back through my postings to the Beaglebone group to see what else I may have done to get it to work without sudo. It too was having that problem but no longer.
With respect to the graphics and LCD displays the issue is more complicated. The RPi pxl library uses fast SPI io features that require PXL.Boards.RPi.pas and there is no equivalent library of routines for the BBB to directly deal with the hardware registers. So the BBB will be slower.
However, the \lazarus\pxl\Samples\FreePascal\SingleBoard\Generic\DisplaySPI doesn't use those and now does compile and run on the Beagle. Just don't have a display connected yet to verify operation and to see if the Lenna.jpg shows up.
The point is that the pxl spi transfer() function has been fixed so programs using it now work with stretch and buster on the beagle and on the Pi. I'm still investigating why the FillByte() function is required.
You asked about showing the screen. I have a small 64x64 bit SPI display. I also have a PiZeroW with the EnviroPi board with display. The code is all Python. I want to port it to Lazarus. (Actually I also have 320x240 SPI screens and some others).
I also want to port this:
https://github.com/botheredbybees/kilnControlleralong with it's parent reflow oven controller to Lazarus.
The more of these types of projects out there the more we can bring people into the much easier Delphi/Lazarus programming world. IMHO.