I see a bunch of people who really got deep into this subject. I never learned too much about it, but I do know this-
out of holes, electrons, and current-current is the one that will really get your attention
I think the main thing is just to consider (as these scientists appear to be suggesting) .... is to think of the universe as some kind of system .... some matrix, and for some unknown reason (simply unknown), there are building blocks.... or more like building 'forces'. So some combinations of these building 'forces' get together (somehow) to form things like fields, protons, quarks, sparks, neutrinos, electrons, photons, atoms, etc. The atoms and molecules appear to be what we 'define' as solid. All these physical 'stuff' is defined by humans --- we 'sense' them, or 'measure' them, or predict them ....and we define them.
In this universe, people don't even know what the origins are..... of electrons, holes, fields, etc. They just know how to define and measure these 'quantities'/'entities' that they see or sense, and know how to make use of them ----- ie. do things with them if they can.
So, as long as something like 'holes' is defined, then just treat holes as yet another physics defined 'thing'. And just use current as whatever it is defined to be by physicists....and use current as it is shown in circuit theory (ie. adopt a convention, and go for it).
As for OP's question of which direction does current flow..... if just focusing on basic circuit theory, just go with most circuit theory text books and use 'conventional' current flow ----- and use a sign convention for voltage, current and power .... aka 'passive sign convention'. You would only get into the hole and electron discussion when entering the physics area.