The issue is that GPIO12 is special and must be held low during bootup.
If you use GPIO12 to control RS or EN it has issues since the hd44780 control signals are pulled up and will override the weak internal pulldown on GPIO12.
This would be an issue on any ESP32 module/board not just this board.
This is presumably part of facilitating a 4-bit control mode.
In short, that board is a complete bodge!
So this is the same circuit as the WeMOS D1 Mini?
The two transistors are J3Y and the signals that feed it are from a CH430C USB to serial chip running at 5V with 5V logic signals.So that is likely causing the collector to float up to 4.1 volts as the logic signals connected to the base and emitter are at 5V.
But the esp32 "mini" style board uses a different design and has 3.3v on the EN and BOOT pins.