I was experiencing exactly the same problem as others on a Win11 laptop. Firmware would not update and kept falling back to old “installed” firmware. After reading multiple posts it occurred to the problem might be the file System on Win11.
I solved the issue by copying the Firmware .bin file from the unzipped download folder to a memory stick and then copying pasting (actually drag and drop) from the memory stick to the newly created USB drive that Ortur created using the 5 sec/reset button sequence.
Worked like a charm.
System:
Edition Windows 11 Home
Version 21H2
OS Build 22000.2538
Windows Feature Experience Pack 1000.22001.1000.0
FYI; during my troubleshooting steps I tried different .bin files that I found on the web, and tried doing it via MS-DOS command prompt using copy command. These did not work.