I have a USB foot pedal doing this, too. I don't have the HID tools installed on the Monterey laptops, so I used Linux to dump some of the details:
lsusb output:
Bus 002 Device 006: ID 05f3:00ff PI Engineering, Inc. VEC Footpedal
USB HID descriptor (hex)
05 0C 09 03 A1 01 05 09 19 01 29 03 15 00 25 01 95 03 75 01 81 02 95 01 75 05 81 01 95 01 75 08 81 01 C0
USB HID descriptor, parsed into a specification:
Usage Page (Consumer), ; Consumer (0Ch) Usage (Programmable Buttons), ; Programmable buttons (03h, named array) Collection (Application), Usage Page (Button), ; Button (09h) Usage Minimum (01h), Usage Maximum (03h), Logical Minimum (0), Logical Maximum (1), Report Count (3), Report Size (1), Input (Variable), Report Count (1), Report Size (5), Input (Constant), Report Count (1), Report Size (8), Input (Constant), End Collection
My pet theory at the moment is that Monterey sees that it's a "3 button" device and assumes it's a mouse, whereas when I do the same dump on a USB mouse receiver, it reports other mouse-related features like Usage (Pointer), Usage (X), Usage (Y), and Usage (Wheel).