Just to follow up, on the "3 commands" . . .
Regardless of how the LCD controller interprets what is happening the program code should be issuing what is essentially three initial 'function set' commands. Don't forget that the 4-bit mode was not originally intended to 'save' I/O pins, it was designed to interface with 4-bit microprocessors such as the Intel 4004.
My opinion is that, since there is no documentation as to what is actually going on inside the controller, we should not try to figure out what each of the individual steps may or may not be doing.
I think we should conceptually group the first three 'function set' instructions together and describe what they are doing as a whole and that is to get the controller into a known state.
Two terms that come to mind are 'reset' and 'synchronization' but there are probably others.
Don