One tag for the whole franchise: the-witcher.
It's fine to define subtags as we've done in other franchises, but there should be one overarching tag so that someone who's interested in the whole franchise, everything Witcher related, can get all of that in a single list or by following a single tag. Also, many questions are going to be about the whole franchise without restricting to books, game, TV show, etc. If someone wants to know something about the Witcher lore, very often they won't care which part of the lore the answer comes from.
Media tags ...
Our usual approach when a single story or franchise has been adapted for different media is to use media tags, for example books, tv, video-games. In this case, things are complicated by the fact that, as you mention, there are two different TV series which are both in the same franchise but independent of each other. For the 2002 one we could create a tag the-hexer (noting in the tag description that it's a subtag of the-witcher and should always be used together with that), but for the 2019 one it's a bit harder because the name of the TV series is the same as the name of the franchise. But maybe the tags the-witcher tv would be enough in this case (we seem to have had no questions about The Hexer anyway), less confusing than creating a new the-witcher-netflix or the-witcher-2019 tag.
