The games(The Darkness 1 and 2) aren't canon to the comics, though they're great on their own. The Witchblade anime isn't canon to the comics neither, though that shouldn't be surprising since the comics are american. They're basically different takes on the comics. I liked them all though.
Especially the anime but you can already see why with a pic like this.
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As for the woke part, Darkness ended like a decade ago and hasn't got a new comic run since. Minus with his daughter, Hope. It missed the woke stuff, thankfully. Not sure about Witchblade though as I stopped reading it after the original ended with Sara.