Factory lube is the best you’ll ever have. As I understood it they bake on stuff on the rollers and pins during manufacture before assembly. I assumed that would be wax based.
Remember, chain wear is roller wear inside. That’s where they lube is important.
The sticky grease on the outside is debateable. I’ve run with it and it’s been fine for me, then as it wears down I’ve applied oil based lubes and gone through the black chain cleaning routine.
However since, I’ve switched to Squirt. Wax based and gets inside and sets. Not as good as factory, but is bloody good stuff. The outside of the chain doesn’t need anything and can appear like it’s got no lube at all. There’s a film of wax in the surface though.
However as the quote from Shimano says, it does make it noisier. I do wonder if a grease like stuff on the surface of a Squirted chain would be better. But then it would draw in the dirt and chain wouldn’t look shiny all the time as I find Squirted chains do.