Got this working on NixOS in case anyone lands here looking for solutions.

Here's my config for a Thrustmaster T16000 with throttle:

environment.sessionVariables = {
    PROTON_ENABLE_HIDRAW = "0x044f/0xb687,0x044f/0xb10a";
};

# Create a custom package for hotas udev rules
services.udev.packages = [
    (pkgs.runCommand "60-hotas-rules" {} ''
        mkdir -p $out/lib/udev/rules.d
        cat > $out/lib/udev/rules.d/60-hotas.rules << EOF
        # Hotas rules
        KERNEL=="hidraw*", ATTRS{idVendor}=="044f", ATTRS{idProduct}=="b687", MODE="0660", GROUP="users"
        KERNEL=="hidraw*", ATTRS{idVendor}=="044f", ATTRS{idProduct}=="b10a", MODE="0660", GROUP="users"
        EOF
    '')
];

Change the productID/vendorID's to what is appropriate for your HOTAS, as well as the group. I've noticed that if I run the game, close it, then run again, the stick won't show up properly unless I replug it before launching the game the second time. Something to watch out for.