Variety has some interesting news in regards to the future of the streaming future of Batwoman:
You The CW is going to be the exclusive in-season streaming home for its new series going forward.
Beginning with this season’s freshman shows, namely Batwoman, Nancy Drew and Katey Keene, The CW series will stream exclusively on its digital platforms throughoutthe full current season. After the season finale of each new show, the full season will be available on the network’s digital platforms until 30 days prior to the start of the next season, at which point they will move to their respective longer term streaming home HBO Max for Batwoman and Katey Keene, CBS All Access for Nancy Drew. Every episode of the CW’s new series will stream the day after broadcast throughout the season.
If you were planning on streaming Batwoman on Netflix, you may have to consider HBO Max.