Basically a sequel set many years after the last book of ASOUE. Which could feature the Baudelaire's in the age of their parents when they died. It could delve on the aftermath of the events that happened in the 13th books. Feature some returning characters, but bring in some new ones. While it wouldn't be a new series to answer the open ended plots of ASOUE, It could delve on things like, What happened to the Sinister Duo? What happened to VFD? Did it regain new safe places and volunteers? With Olaf gone, maybe some of the evil has subsided without him constantly doing wrong doings. Do the remaining survivors help to regain the volunteer side of the world or let it fall apart and get destroyed?
While the Baudelaire story can be left alone for good, I do love the story of VFD and everything else in these books. That's why I'm so glad a new series setting as a prequel is coming out.
I feel like the Beatrice half of The Beatrice Letters more or less is this. It's set many years after the end of ASoUE and sheds a little light on what happened afterwards without, I feel, undermining the deliberate non-closure of the main series - we're not meant to have an authoritative, authorial edict explaining everything that happened, it's up to us to decide, or to decide that the characters are now free from the constraints of the narrative and can live their own lives. With that said, if there ever was a true sequel to ASoUE that addressed some of the open plot threads, it would be as you say - set a considerable amount of time later, and starting out as a fresh story.
Edit: As for ATWQ, Handler's said somewhere that it's actually almost mocking the idea of a prequel, and I interpret that as being because it's such a distinct story that exists only on the fringes of ASoUE. In fact, it looks like an actual, directly relevant prequel plotline is happening with Kit back in the city, and Lemony is isolated from it.