> but I couldn't find any obvious way of adding issues to a project from the issue itself rather than from the project view.

You can add issues to the old Projects from the issue view the same way as the new Projects (beta), it just takes 2/3 clicks for both: On the right sidebar in your issue you have "Projects", then a dropdown of your projects, and then you can (optionally) select the column where to place them (without that selection, the land in some kind of inbox inside the board).

I am using CodeTree for the list view of issues in milestones. The new Projects (beta) unfortunately also only offers that via the in between step of manually adding issues to a project and then "tagging" them with the milestone again as an attribute I think :/