This is a sketch for an Arduino Pro Mini-based adapter that converts DualShock 2 controller signals into XInput! This way, you can use PS2 controllers on any PC without extra software.

Required Hardware

Arduino Pro Mini
Microswitch to reset the Arduino
PS2 controller extension cable (you'll need to cut off the female end of this cable to solder its wires to the Arduino)
0.96in display (optional) The linked parts are only references; feel free to use any compatible hardware or to edit the sketch to suit your hardware. No affiliate links.

Diagram

Note on Flashing

Flashing the XInput library makes the Arduino unresponsive to further flashing.

Wire a switch between GND and RST to act as a reset switch
Enable verbose output on upload in Arduino IDE -> File -> Preferences
Select the COM port of the board and the corresponding board type as provided by the XInput library. For me, this was Arduino Leonardo w/ XInput
Press "Upload"
Once the notification in the bottom right says "Uploading", press the reset switch twice in quick succession
On success, the output window should print out data, concluding with "avrdude done. thank you." You'll need to perform steps 4-6 on every flash as long as you have the Arduino configured for XInput. Find more information about this in the readme of the Arduino XInput library.

Required Libraries

PS2X library for interpreting the controller's signals
ArduinoXInput_AVR library for sending XInput commands via an Arduino Pro Micro
Adafruit_SSD1306 library for display output

Sources

PS2 controller wire diagram by Bill Porter
Gamepad Tester for testing the controller in a web browser