The token copies exactly what was printed on the original artifact and nothing else (unless that artifact is copying something else or is a token; see below). It doesn't copy whether that artifact is tapped or untapped, whether it has any counters on it or Auras and Equipment attached to it, or any non-copy effects that have changed its power, toughness, types, color, or so on.

If the copied artifact has {X} in its mana cost, X is considered to be 0.

If the copied artifact is copying something else (for example, if the copied artifact is a Sculpting Steel), then the token enters the battlefield as whatever that artifact copied.

If the copied artifact is a token, the token created with Cogwork Assembler copies the original characteristics of that token as stated by the effect that that created that token.

Any enters-the-battlefield abilities of the copied artifact will trigger when the token enters the battlefield. Any “as [this artifact] enters the battlefield” or “[this artifact] enters the battlefield with” abilities of the chosen artifact will also work.