Is it referring to the settings, embark profile, world generation…?

In short, yes. Stock (I'm pretty sure) refers to the game exactly as it is downloaded.

To clarify, Stock refers to all three of the things I listed? If so, then why does one of the guides suggest setting (among other things) the world size to small? Sounds to me like that shouldn’t be allowed under this definition of “stock”.

Oh, not world generation, since that requires no extra setup. In other words, there is no default world size.

It refers to no mods such as dfhack, dwarf therapist modifying the game outside of the game essentially ... use your best insight and read into the spirit of the rules.

What is the spirit of the rules? Can you modify mineral scarcity? Cavern number? Z levels? Savagery? Rainfall? Drainage? Night creatures? Titans? Number of civilizations?

I would think that any options available in game would be allowed to be changed. I don't really see any issue with this because world gen is already part of the timing so any of these setting changes would be timed and recorded as well.