Foxidna stated that there are 5 secret rules Shaula has for protecting the tower in Ep. 71, and judging by Shaula’s reaction, Foxidna was almost certainly right on the money, meaning Shaula saying that there’s no fifth rule may have been a lie with Foxidna pointedly asking if that’s the last of them meant to show her belief that there’s definitely one more, showing again that she’s probably a soul clone of Echidna given Echidna was from that time period of four hundred years ago.
And as we see from Ep. 73, Shaula herself believes that Emilia bears a striking a resemblance to Satella, which is why she wouldn’t mind becoming the half-witch’s apprentice, which is a comment showing both that she knew who Satella was and that she was a witch, likening Emilia to Satella. Given this, I believe it’s plausible Flügel had a very good reason to hold Shaula to this if that’s indeed the fifth rule.
Thus, Flügel may have ensured Shaula can’t directly comment on Shaula’s appearance, possibly ’cause of a future situation in which Satella or the Witch of Envy appears, such as an exam in which a much weaker version of Satella appears or much like in Season 2, Satella and the the Witch of Envy appear in the Dream Castle/Sanctuary due to the Taboo, and this was done to prevent Subaru or the others from losing trust in Emilia later.
Given we’ve already seen one instance of the Taboo being invoked when amnesiac Subaru’s heart was stroked and calmed down in Episode 74, likely due to the presence of an enemy, such as a Sin Archbishop of Gluttony, that may have also stealthily psychologically primed viewers to expect that to happen again given he has no idea what the Taboo is and what situations allow for Satella or the Witch of Envy to appear.
As to hazard a guess what Flügel specifically told Shaula, it may have been something along the lines of “One day when I return, and you see someone with a striking resemblance to Satella, you are not to directly comment on it under any circumstance whatsoever, and you are forbidden from revealing this rule to anyone. The other four are okay, but this one is absolute no-go territory. Do I hear an okay?”
As for what Shaula’s true purpose is, I think it’s somewhat like Season 2 Tea Party Echidna’s, only her role is split between herself, Foxidna due to all the suspect things she’s done, and perhaps the unseen force I believe was spying through the birds that led Foxidna, Subaru, and Julius to the hidden passage to the balcony to develop the cast in a certain way for a larger plan to steer the world to a good future.