TBH, I never noticed the issue of the icons not lining up along the bottom, but now that it's been pointed out, it does seem a bit awkward. It's not something that prevents me from using the app, of course, but it might be nice to address it.
Out of gopi's two mockups, I prefer the one on the left, but actually I would address it a different way. Make the two boxes the same size. The one on the left can be just like it is now, with the pen. As to the one on the right, rather than say 'Inbox' above it, which causes the issue by pushing the box down, just put the word 'Inbox' inside it when the inbox is empty, and have the number of inbox items when it's not empty. I can't draw, but what about something like:
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