When do the books and the games diverge?

The first game takes place a few years after the last events of the book series. This should be the main point of divergence, as Andrzej Sapkowski explicitly stated games are a completely separate continuity - at least according to him.

You said the author is continuing to write - that's not true. The series was finished in 1999, with The Lady of the Lake, but it's only been translated to English very recently (2017). He has written one book since, Season of Storms, in 2013 (with official English translation bound in 2018), but it is more of an interquel, because it is set somewhere between the first two books (The Last Wish and Sword of Destiny). It doesn't touch the continuity of the games for the most part - although its epilogue is set way into the future, it doesn't contradict the games, and vice versa.

TL; DR: there's no real divergence to speak of, except some minor creative decisions taken by the game designers. Overall the games and the books match.