Logitech G27 is not detected by Proton versions newer than 4.2

While trying to reproduce #4441 I encountered a slightly different problem:

I have a Logitech G27 and it gets detected only with Proton 4.2, but it doesn't with Proton 5.0 nor Proton 5.13.
My issue seems to be very similar to this one https://github.com/ValveSoftware/Proton/issues/2366#issuecomment-620913710

This is the Proton 4.2 log of Project CARS 2 Demo:
steam-737770_4.2.log

And this is the log with Proton 5.0:
steam-737770_5.0.log

So far I tried Project CARS 2 Demo and F1 2018, and both presented the same issue.

And for the record, with native Linux games (Euro Truck Simulator 2 and DiRT Rally) the G27 is successfully detected.

I'm using Arch Linux as my OS with the latest Steam beta client.

Start by comparing the attached Project CARS 2 Demo logs for Proton 4.2 and 5.0, focusing on the Logitech G27 detection difference. Reproduce the behavior with Project CARS 2 Demo and F1 2018, compare it with the native Linux games listed, and consider the issue resolved when newer Proton versions detect the G27.