Unless I've misread this entire thread I think there is some confusion here...
Check the Firmware Updater readme...
I can only speak for my SKR 1.3 and SKR Mini E3 32 bit boards but I use this plugin to update them both regularly.
After installing and configuring usbmount (in my case, yours may be different depending on the printers MCU) on OctoPi I can see the printers SD Card as a directory on the Pi, viz: -
pi@octopi:~ $ ls -la /media/usb0
drwxr-xr-x 3 pi pi 32768 Jan 1 1970 .
drwxr-xr-x 10 root root 4096 Nov 29 19:08 ..
-rw-rw-rw- 1 pi pi 249732 Dec 19 08:28 FIRMWARE.CUR
drwxr-xr-x 2 pi pi 32768 Aug 14 2019 'System Volume Information'
"Firmware Updater" copies the new
firmware.bin file to this directory and "reloads" the printer to install it.
So whilst the firmware IS being upgraded using the SD Card it's not necessary to remove the card from the printer and do this manually...
The trick is to get usbmount or whatever configured correctly to mount the SD Card so Firmware Updater can talk to it!