That kind of jumped out at me too because like you said Anakin=Vader was not widely known at the time this was happening. It really has me wondering who Baylan is.I'd have to re-watch the episode, but was Baylan referring to fall of Anakin and the brief time period where he murdered younglings and the Separatist leaders or the broken man being kept alive by machinery?
There's supposed to be only a small handful people that knew Anakin survived his duel with Obi-wan and was in the suit. The Emperor, Obi-wan and maybe Yoda pre-ANH, Luke in ESB, Leia in ROTJ. Ahsoka found out during her duel with him. Thrawn figured it out, and Takin suspected Vader was Anakin. Reva threw it out in the Obi-wan series as a way to taunt Kenobi, so that is technically how he found out. Although the explanation for how she knew for certain was never clear. Even after Luke and Leia found out, it didn't become public knowledge until almost 25 years after Endor per the canon novel Bloodlines.
Also I love the character of Baylan, as much as it sucks that the actor passed this year I really hope they recast it because that story arc could get really good.