Yes, it supports nested tags, and the tags create structure that suggests directory nesting. However, as far as I can tell the search can't be made to honor the nesting.

To make my example explicit above, suppose I have a "directory" structure with dirs like `conf`, `conf/iaq2016`, and `conf/gmu2012`. Then a search in `conf` will not turn up results in `conf/iaq2016` or `conf/gmu2012`.

Believe me, I check this once every few months, always hoping that google will have improved their "tag" implementation.

I do appreciate your tip about multiple browser windows, though. In general, I don't like having multiple windows open to the same application-- but that's my problem, and not a design flaw in Gmail's search.

Yup. Nested labels like "top/med/bot" get flattened to "top-med-bot" for search, e.g. in:top-med-bot keyword