The key to this is to understand that the Bluepad32 “library” for the Arduino IDE and ESP32 is actually included in the alternative version of the Arduino-ESP32 core that the author provides. See documentation.
The board URL that they make you install in the Arduino IDE (https://raw.githubusercontent.com/ricardoquesada/esp32-arduino-lib-builder/master/bluepad32_files/package_esp32_bluepad32_index.json) then points to the package https://github.com/ricardoquesada/esp32-arduino-lib-builder/releases/download/4.1.0/esp32-bluepad32-4.1.0.zip which is just a packaging of Arduino-ESP32 with the Bluepad32 library included.
You need to tell PlatformIO to use that as the Arduino-ESP32 framework package instead of the regular framework-arduinoespressif32 package. The .zip file I linked to already has a package.json for inclusion into PlatformIO. Sadly however, the name field of the package was changed to framework-arduinoespressif32bluepad32, so it will be rejected as a replacement for framework-arduinoespressif32 until renamed. (Otherwise,we could have referenced the release zip directly.)
Thus, I simply renamed it back to framework-arduinoespressif32 and reuploaded it here. With that, I can then tell PlatformIO to simply use this as the Arduino core package.
[env:esp32dev]
platform = espressif32@6.10.0
board = esp32dev
framework = arduino
; reupload of https://github.com/ricardoquesada/esp32-arduino-lib-builder/releases/download/4.1.0/esp32-bluepad32-4.1.0.zip
; but with package.json's "name" field renamed back to framework-arduinoespressif32
platform_packages =
framework-arduinoespressif32@https://github.com/maxgerhardt/pio-framework-bluepad32/archive/refs/heads/main.zip
You can see that the Controller.ino example compiles perfectly fine with this configuration then: