A few usability suggestions
Great new design, I like it. There are a few things that I think could be improved:
Ads look the same as new emails so its hard to see how many emails you haven't checked - good for ads click through, not so great for user experience.
The inbox icon doesn't show the number of unread emails which is a bit odd.
The inbox default to Priority not All even if you haven't set the priority emails.

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Laura Rogers commented
I don't like the new design, for a number of reasons, but one of the reasons, which is pointed out in the main comment, is that the inbox doesn't show the number of unread emails. This is critical information to me as I don't always open all of the necessary emails I receive every day. I use the "unread" number to let me know that I may need to scroll down further to find the emails that I've mentally prioritized for a later date.
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Alexander commented
I agree with Alexandra.