Warning! SPOILERS for Batwoman season 3, episode 7
The Batwoman season 3 mid-season finale confirmed that Swamp Thing exists on Earth-Prime following Crisis on Infinite Earths. The Guardian of the Green was previously established as being a part of the Arrowverse, with the events of his short-lived series on the DC Universe streaming service being established as having taken place on Earth-19 of the Post-Crisis Arrowverse. However, this marks the first confirmation of Swamp Thing existing on the same Earth as the other heroes with shows on the CW.
The main plot of Batwoman season 3 focused upon the recovery of various "Bat-Trophies," largely consisting of weapons that Batman had acquired from his enemies over many years of crime-fighting. This led to a number of new enemies armed with the weapons of classic Batman villains emerging to menace Batwoman's Gotham City. It also led to the reemergence of Poison Ivy, who had been buried somewhere underground by Batman over a decade earlier, but who also found a way to user her mind control powers to plant her consciousness in other bodies.
As Batwoman season 3, episode 7, "Pick Your Poison" opened, it had become apparent that Team Bat's medical expert, Dr. Mary Hamilton, had become the latest host of Poison Ivy. Ryan called in a favor from her biological mother and business rival, Jada Jet, asking for her company's help in crafting an antidote that would cleanse Mary of the influence of the Arrowverse's Poison Ivy in Batwoman. When Jada asked her scientists for an update on how the Poison Ivy antidote was progressing, the scientist replied (in reference to Mary's blood sample) that nobody had seen "a plant-based infection like this since Swamp Thing."
This marked the first time that Swamp Thing had been confirmed to exist on Earth-Prime, which is the central world of the new Arrowverse following the Crisis on Infinite Earths crossover event. Reportedly, producer Marc Guggenheim tried to set up a scene teaming Swamp Thing with Matt Ryan's John Constantine as part of Crisis on Infinite Earths, but the legalities couldn't be worked out in time. The best they could manage was a brief Swamp Thing cameo in Crisis on Infinite Earth's final episode. As it stands, the only semi-official reference to Swamp Thing on Earth-Prime lies in an augmented reality Easter egg in Constantine, where viewers could call the real-world phone number on John Constantine's business card and be treated to a voicemail where Constantine told anyone who was looking for Alec Holland to "try the bloody swamp!"
Sadly, those fans hoping for a Swamp Thing cameo as part of Batwoman season 3 seem sure to be disappointed. The live-action rights for the character (along with the rights for John Constantine) are believed to be tied up in plans for J. J. Abrams Justice League Dark series. This means that Ryan Wilder probably won't be able to count on Alec Holland's aid in saving Gotham City and her best friend from Poison Ivy.