She has an agent give you the Burned Book Of Law the first time you sail away from Neketaka so she can talk to you in secret- she's not allowed to manifest to you separate from berath, but by using the Book you are initiating contact with her, and there's no rule against that. She implies that the gods barging into your dreams to squabble is at least partially for show, and that they're keeping an eye on how the Deadfire responds to Eothas as a test to see how mortals have done under their guidance. Woedica wants to use you as a proxy for all mortals, to determine whether mortals are doing well or will need the rule of an iron fist in the times to come. She'll answer general questions about the lore, some of which are nice to have if largely inconsequential: the DLC crown belonged to her favourite inquisitor and bore a piece of her soul, Izzia(the smith who puts the crown together for you) is a soul descendant of that inquisitor, Hollowborn were a lot more common before the Wheel along with sundry other soul maladies, etc. She spills the beans on the Wheel being artificial pretty much right away, which I think is a mis-step, but at least she doesn't mention Ukaizo before you learn that Ukaizo is important. As you progress through the main quest you can talk to her at any time via the Book, and she'll comment on various main and faction quests, including the DLCs. Her repertoire of discussion topics will open up as well, and she'll chat about the Guardian and the apotheosis project. She'll also either praise or berate you, presumably based on how you solved quests but I have no idea what criteria is being applied. The final god conversation on Ukaizo ends with her sticking around after the rest of the gods leave to comment on how you did as the mortals' advocate- siding with any faction annoys her as any sign of fellowship and co-operation makes it harder for her to plead her case to the others. The additional dialogue with Eothas after this suggests that she's considering making a successor to Thaos, whether you like it or not, and Eothas is disturbed to hear that Woedica has plans. While I'm here, Eothas now also reveals that the natural process of reincarnation was broken by the creation of the artificial one and won't just resume when the Wheel is destroyed, the Godhammer badly damaged him and he was barely able to possess the titan(the release version of the game hints but never confirms that his strength is so low that the effort required to break the Wheel will kill him), that he wanted to do it while the faction war was still looming over the Deadfire to encourage diverse mortals to come together, and that he's sorry he destroyed your castle but you need to get over it.