If the removal of the content is the point, then a soft delete like you mention (assuming hard deletes are a problem) should be applied on all of the content, and all of these topics & posts should be excluded from the default backup. Instead, when you do the archiving, they should be put in a separate “Archives” backup of their own.
If you just don’t want your searches getting polluted & slowed down with deprecated posts, and you don’t want archived categories cluttering up your category list, then a “do not search” flag on archived post and a special category that doesn’t show even in staff lists (but retrievable through admin panel somehow) would suffice. Essentially making all topics Unlisted, plus special treatment of the category visibility.
We’ve talked about similar things before: