I have this in my additional boards manager URLS

https://dl.espressif.com/dl/package_esp32_index.json

I'm on Mojave though

Yes you are propably right the relay takes too much current for the DO
Why do you need this relay anyway
If you do need it why not use a simple transistor to run the relay. This uses 12V but 5V relay will do what you want

Serial.available() returns the number of bytes available to read.

Have a look at this. Ordinary SPP may not assist
https://learn.sparkfun.com/tutorials/bl ... h-profiles

Did you connect with the App I suggested? It is SPP.

Try using a cell phone app like "Bluetooth Terminal HC-05"
If you can pair and receive data with this from the trackpad then you can do it with an ESP32.
Its my goto App for looking at data streams from BT

Can you show schematic of how the ESP32 gets supplied. ESP32 are 3.3V. I assume you have regulator inbetween. What is the input range of the requlator. See previous answer

I assume that you are using classic bluetooth to receive data? If so have you has a look at the data stream? Have you implemented routines to make sure that all the bytes of a single message are transferred and received. From my experience BT often breaks byte transfers and hence the receiver cannot...

I use Pin 34 for RXD-0 35 for TXD-0 27 for RXD-2 28 for TXD-2

Works fine
Have you seen this?

Two different manufacturers?