You can get USB based GPIO boards for ~$20. Some need drivers, some emulate serial. I'm guessing that with a USB-to-go cable, you could connect these to the phone.
Then you're back to $30 and can just buy an ESP32 with a screen module but suffer from the indeterministic USB stack. However you could also buy a $6 ESP32 and let it communicate with the smartphone over blue-tooth at a price point of $10 (phone) + $6 (ESP32).