If you followed the Linux/Other/UEFI Shell update instrutctions of “Framework Laptop 16 BIOS and Driver Releases” page, Framework Laptop 16 BIOS and Driver Releases, the extracted files of the Bios update zip file should appear on the fat32 formatted usb drive as 1 folder and 3 files, is this what you had (there will be a hidden folder if you are also showing hidden files). With TPM set as hidden, in the BIOS, I had the usb drive appear in the Boot choice in the F12 Boot selection.
Select it, and I think the update worked automatically from there.