Marked and leech are tags, though, and not card properties. Moving them out of the tags section will only add to the confusion.
I’m not a fan of a subsection, either, because it would erroneously suggest a name like “Builtin::marked” and would require a lot of special casing. And what would happen to children of these tags?
As @dae has said, users complain about the predominance as well as about the inconspicuousness of the builtin items. This may suggest that the status quo is a reasonable compromise.
What about leaving the items where they are but making them more eye-catching with font styling or special icons? It might make a huge difference if the icon for “marked” was a star as in the reviewer. “Untagged” could have the tag icon but crossed out and I’m sure we could come up with appropriate icons for “Current deck” and “leech” as well.
Other than that, saved searches are definitely an underused feature, even by more experienced users (like myself). This discussion is an exemplary use case for them, but I don’t know how people could be nudged to make better use of them.
Something that I try to keep in mind is that what is intuitive to existing users may not be for new users, and vice versa. I wonder if the fact that you’re getting lots of questions about marked and leech is really a signal that these belong up the top, or whether it’s more that they used to be up the top, and that’s what users are used to. The messaging could be improved here - if the tooltips shown when marking or leeching a card were something like “Tagged note with ‘marked’” and “Tagged note with ‘leech’”, then it should be more obvious where to look to locate them.
That is not a bad goal in theory, but we also need to consider progressive disclosure so that the user is not overwhelmed with options, and figuring out where things should go and how they should be categorized is not always easy.
I’m a new Anki user, I’ve just used it for three months (althought for many hours a day, that’s true) and 2.1.43 was the first version I used, so I don’t even know how “leech” and “marked” were displayed before.
I personally don’t see anything wrong with the way they are displayed in the browser; quite the contrary, the fact that “leech” and “marked” are shown as regular tags in the browser helped me to understand how those features actually work, and how I could use them.