TLDR; Bricked a 2nd Pico for this project.
Designed a simple single layer PCB for the display and the Pico.
Milled and soldered. Everything worked correctly. For 5 mins.
After that, the USB device kept getting disconnected and reconnected.
After a lot of experimentation of what might went wrong, it seems that
the Pico was bricked when desoldering the pin headers. To rule out any
possible bugs in my code I loaded the USB device_hid_composite example
from the SDK. The device behaves the same.
Ordered another Pico as well as a Waveshare RP2040 Tiny board.
The RP2040 Tiny might be a better choice for a v3 of the PCB as it allows for arbitrary placement
of the USB port on the pendant’s enclosure.