@JimmyHalibutOn the upside if it's a problem getting steam to recognise the joystick then that's a totally different issue to getting it working in game. In some cases people had it working in other games even when steam didn't see it, or they had to disable Steam Input for it - it all varies by configuration.
There was a related guide for Logitech hotas x56 here, it seems to be a common problem between that and Steam.
https://www.reddit.com/r/EliteDangerous/comments/hkkkv9/pcsetup_setting_up_my_saiteklogitech_x56_hotas/
I haven't been through that guide as I don't have that setup but it might help you with steam.
If I was in your case, I would be using x360 or xoutput to map the hotas as a single xbox controller, then use that virtual xbox controller inside of steam - and if that doesn't work because too many controllers, then using hidhide to mask the hotas from the system. Hopefully it works before you need to do that last bit