At some time JKR will surely sue to protect her reputation.
My thoughts too.
My guess is she's never wanted it to get to that point and to be seen as vexatious. Optics are important here as much as legal out comes. Even if she wins a legal case she could lose the war if a case were to trigger a public backlash against her and encourage MPs to change the law in response. Or for her to become used as a political football by various political parties to worsen the already existing culture war.
For that reason it makes more sense for her to bid time pending outcome of other legal cases in the uk, which will then strengthen her hand if she does decide to go down this root. It also gives an opportunity to judge changing public opinion and the level of support she has.
She's aware of legal ramifications stemming from any case she brings as well as the pressures on her personally from doing it and the Barbara Streisand effect it will create from such a high profile case those.
Hence why she possibly has not done so yet.
But i do think it will reach a point where she's left with no choice. And she will make a move at a point where public frustration with the culture war hits a high with moderates.
The interesting reflection on this was Nancy Kelly's really very obvious avoidance of accusing JKR of being transphobic. The way she answered was noteworthy. I found that very telling and it did make me wonder if discreet words behind the scenes have been voiced indirectly.
So I do think it will come. But only after she feels that it will make a positive change rather than risk making the whole situation worse.
She's smart. And she can afford to pick a moment to her best advantage. If she brings a case its important but the timing and choice of defendant is perhaps even more so.