Should a new tag be created such as
ftl-advanced-edition for these types of questions, or should questions related to "classic" FTL be edited to reflect the new Advanced Edition content?
FTL: Advanced Edition does not seem to be a DLC or expansion - it's just a big content update to the base game so you should update existing questions and answers instead of adding new ones. I don't think there's a need for a new tag for it.
There is already a method for dealing with questions that need an update due to a major change in the game: offering a bounty. There's even a bounty reason specifically for this occasion.
Current answers are outdated The current answer(s) are out-of-date and require revision given recent changes.
This should cover all the questions that are 'no longer relevant' due to the update, and any questions specific to update content can be addressed by individual questions.