I lean towards setting up the Pico W and the OT-2 with MQTT. You can either use an external orchestrator that communicates with the OT-2 and Pico W (ideal), or use the OT-2 as the orchestrator to send commands to the Pico W.
If due to network/WiFi constraints, you can’t use a Pico W, a suitable alternative would be to get a Raspberry Pi Zero 2W (reasonable price) and connect it to eduroam/university WiFi/etc.
From what I can tell, even though a Raspberry Pi 3+ is at the core of the OT-2, the digital IO pins from the RPi don’t seem to be exposed.
@jeff.watchorn has experience integrating external devices with the OT-2 and may be able to shed some additional light.
I tend to shy away from writing custom serial communication protocols and drivers usually intended only for Windows or MacOS. If it’s a “plug together”, download some code, and “here’s the Python API” setup, great - otherwise it can be pretty time intensive IMO. Setting up two independent devices for control via an external orchestrator is a compelling concept to me from a setup, robustness, and modularity standpoint, at least for when time synchronization on the order of 10’s of ms isn’t absolutely essential (see also Improvements to the Digital Pipette - #8 by chattrick)
https://support.opentrons.com/s/article/Integrating-the-OT-2-with-other-lab-equipment