Batwoman was never in danger… haters who wanted it to fail before it even premiered and clicbaiting sites tried to spin it as “in trouble”, but the truth is that is was the second highest rated show on the CW. They would have been crazy not to renew it. I mean don’t get me wrong, if someone dislikes it that is fair, we can’t all agree on everything. But it is not a struggling show limping along that was lucky to get renewed when it was failing. That was objectively never true.
Supergirl is apparently tied for fourth best show, so not shocking it got renewed. The rumors of next season being it’s last are fuel largely due to the fact everyone contract is up after season 6 and will have to be renewed. Obviously so long as Melissa Benoist wanted to renew they could keep going and just bring in new characters. Half the cast from season 1 has already left. But with it being the ranked fourth and the possibility it could go down next season, it is possible that they won’t be able to settle on enough money to both make her happy and keep the show profitable. But unless the ratings sink next season betting they will try when the time comes to re-negotiate.
Supergirl and Batwoman are doing good, The hater want it to be some black eye on the network that is lucky to survive but it isn’t regardless of anyones personal feelings on the show they are objectively successful.
Legends I will admit gets rumors of it being cancelled every season and speculation, so believe it when it is officially announced. But it is the lowest rated of the Arrowverse and the most expensive to make per episode. So if anything was in danger it was that one, although CW keeps renewing it well ahead of time so clearly they are happy with it.