Karn can still find artifacts in the sideboard for a number of reasons. First, Karn can find *artifacts*; it doesn't matter what color those artifacts are. He can grab a Pithing Needle or a Silent Submersible. The color is irrelevant which means Painter's Servant is irrelevant.
Also, Servant will not change the color of anything in your sideboard because none of those cards are ones affected by Servant as Servant only applies to cards in the game and cards in a sideboard are, as Karn alludes to, outside the game. Servant *does* affect the color of cards in Exile but, as mentioned above, that doesn't matter.
and artifacts in sideboard
Painter's Servant
Grindstone (I know this isn't relevant but your title includes it so I am including it)
Karn, the Great Creator
Karn can still find artifacts in the sideboard for a number of reasons. First, Karn can find *artifacts*; it doesn't matter what color those artifacts are. He can grab a Pithing Needle or a Silent Submersible. The color is irrelevant which means Painter's Servant is irrelevant.
Also, Servant will not change the color of anything in your sideboard because none of those cards are ones affected by Servant as Servant only applies to cards in the game and cards in a sideboard are, as Karn alludes to, outside the game. Servant *does* affect the color of cards in Exile but, as mentioned above, that doesn't matter.