Do you see a chance to check somewhere if the Argon ONE case is working right with a HDMI monitor or TV?
I‘m asking, because sometimes in the past it was only an issue of the correct assembling of RPi with the case pcb. A little bit of controlled force is needed to connect right with this micro HDMI and USB-C connectors. Unfortunately there were also problems with bad soldering points.
I’m afraid you have to play a little with manual set the display resolution via cmdline.txt. The newer kernel versions are very sensitive to the EDID data. In combination with your VGA adapter, these could be missing or may be incomplete.
Within the case, the power is supplied via GPIO pins, not via the USB-C. That could cause a difference in timing while switching on.
Try to append this to the kernel line in the /boot/firmware/cmdline.txt video=HDMI-A-1:1280x1024M@60D