While mapping the gyro to 'cemuhook' works while emulation is active, there is currently no way to use direct gyro input concurrently with Steam bindings on programs that support DSU - as far as I can tell.
There have been options for the use-case in the past, like this multi-platform app by FrogTheFrog; however, that's built on an almost 4-year-old version of Electron(which crashes on app start with the GPU sandbox enabled on my system), the Linux version seemingly isn't able to get data from a wired Steam Controller - and most importantly, it's been archived by the author.
There's newer options for other gyro-enabled controllers and the Deck, but none that seem to support old gordon.
P.S.: While beyond the initial scope of this feature request, it would be in line with current Steam Input developments to add the capability to apply a simple, but effective filter to the raw data like the 1€ Filter - before relaying that information to the DSU client.
FrogTheFrog's app allowed for simple low pass/high pass and Kalman filtering, which were generally hard to configure, and led - consequently or not - to mixed results.