I'm happy to report success using the similarly named fwupd Homebrew formula on an M1 Macbook Pro (
https://formulae.brew.sh/formula/fwupd) (
https://github.com/fwupd/fwupd).
My process was:
1) install the formula
brew install fwupd
2) run the following (note the command "fwupdtool" instead of "fwupd" or "fwupdmgr")
sudo fwupdtool get-devices
sudo fwupdtool refresh
sudo fwupdtool get-updates
sudo fwupdtool update
3) disconnect the dock's Thunderbolt cable, and keep the dock connected to power
4) wait ~1 minute for the firmware update(s) to apply and the dock to reboot (during which you can reconnect the Thunderbolt cable or keep it disconnected)
Be aware that after step 3 the LED indicator at the end of the dock's Thunderbolt cable will remain off, even when plugged into the Macbook during step 4, until the dock applies the new firmware and reboots. Definitely keep the dock powered throughout this whole process; I don't know if the dock will recover from interrupted power during a firmware update and I did not care to find out.
Hope this helps!