I personally don't care for nested tags. It's too cluttered, because even if focus on tags starting with project2, there's a lot of verbosity. What I do is analogous to a "working directory" where everything is relative to that directory. For instance, rather than #project1/tag2, if I click on #project1, the project1/ is prepended to all the tags automatically inside storage but hidden in the display of notes. Implementation is simple. If using Javascript, store the current project name in a variable and prepend it when relevant.

Edit: Another advantage of this is that cross-project tagging stands out because the full tag is displayed.