If fwupdmgr get-updates isn’t finding the update yet, you can download the .cab file from LVFS: Laptop 16 Keyboard - ANSI and then run fwupdmgr local-install filename.cab (i.e. fwupdmgr local-install 53bafa8c884106d1d996201a5f672c612a563880fdfef18448b823b9692dbcb6-framework_ansi_0.31.cab). No need to figure out how to copy files without a working keyboard.
P.S. That’s for the ANSI keyboard. Numpad link is LVFS: Laptop 16 Numpad, and if you have other keyboards then follow the links from Keyboard Firmware Update (Framework Laptop 16) to get the appropriate .cab file.