No. The WH-1000XM4 does not act as a USB mass storage device for firmware. The USB-C port is for charging and audio passthrough only. You must use Bluetooth and the Sony Headphones Connect app.
If you tried the update and saw an error message (usually "Update failed – turn off headphones"), do not panic. Here is the recovery sequence: Sony Wh-1000xm4 Firmware 2.5.1 LINK
Firmware 2.5.1 is a software update released by Sony for the WH-1000XM4 headphones. The update aims to enhance the overall performance and user experience of the device. According to Sony's official release notes, Firmware 2.5.1 offers several improvements and new features. You must use Bluetooth and the Sony Headphones Connect app
However, if you are looking for the for troubleshooting or to perform a manual recovery using a service cable, you will need to use community-backed archives. The update aims to enhance the overall performance