I think I found a solution at least for my case, this worked for me on debian bullseye running Klipper and KlipperScreen for 3d printer controls. What's strange is the terminal doesn't show on the display on initial boot and shutdown but once it boots to the KlipperScreen everything works as normal. Hopefully someone can build upon this to get full functionality.
I noticed when I ran xrandr two resolutions were listed for the BTT screen, 1024x600 and 640x480
Screen 0: minimum 320 x 200, current 1024 x 600, maximum 16384 x 16384
HDMI-1 connected primary 1024x600+0+0 (normal left inverted right x axis y axis) 800mm x 450mm
1024x600 59.99*+ 59.99
640x480 60.00 59.94
I then tried switching to the lower resolution
xrandr --output HDMI-1 --mode 640x480
The display worked but was offset and touch wasn't aligned
I found this post to add custom resolutions https://unix.stackexchange.com/questions/227876/how-to-set-custom-resolution-using-xrandr-when-the-resolution-is-not-available-i
I then tried to add a custom resolution, first getting the parameters of the screen
gtf 1024 600 60
this returned the parameters # 1920x1080 @ 60.00 Hz (GTF) hsync: 67.08 kHz; pclk: 172.80 MHz
Modeline "1920x1080_60.00" 172.80 1920 2040 2248 2576 1080 1081 1084 1118 -HSync +Vsync
create the new mode
xrandr --newmode "1024x600_60.00" 48.96 1024 1064 1168 1312 600 601 604 622 -HSync +Vsync
add the new mode
xrandr --addmode HDMI-1 "1024x600_60.00"
change the output to the new mode
xrandr --output HDMI-1 --mode "1024x600_60.00"
this got the display up and working with touch enabled too.
these settings are reverted upon reboot so to set these to default you'll need to create a monitor.conf using a text editor, using nano in the example below
sudo nano /usr/share/X11/xorg.conf.d/10-monitor.conf
then enter the code below, replace any details for Device or Modeline
Section "Monitor"
Identifier "Monitor0"
Modeline "1024x600_60.00" 48.96 1024 1064 1168 1312 600 601 604 622 -HSy>
EndSection
Section "Screen"
Identifier "Screen0"
Device "HDMI-1"
Monitor "Monitor0"
DefaultDepth 24
SubSection "Display"
Depth 24
Modes "1024x600_60.00"
EndSubSection
EndSection
Save and reboot and it should be up and running.