The new nav bar is interesting. As has been said, it's more attractive and a lot more functional than the previous version, but there is a bit of a learning curve - I can easily imagine that some people don't find it completely intuitive at first (and of course that's what you want it to be).
So for example, what if I select the combined inbox and then want to go to one of my accounts? I know that the trick is to press the 3 dot icon next to the words "combined inbox", then select the account that I want, but it wasn't
obvious - at least for me there was an element of trial and error in discovering this. Now once you know this it probably becomes second nature, the question is whether that's sufficient? I don't think this is a matter of the icon, because I can't offhand think of an icon that would make it obvious. Maybe the words "expand" and "hide" would be a little more obvious, but I do actually quite like the icon once I've worked it out.
The tricky bit is that what's intuitive for one person may be obscure for another. For example, the first time I selected a folder then wanted to go back, and couldn't see what to do, my instinct was to try the back button. But I don't know whether that is something others would think of doing, nor what the correct behaviour should be if someone does that (go "back a level" from whatever was last selected I guess).
One that I did find a little odd: when I selected one address from the "People" list where I didn't have anything from them in the inbox (because I'd archived everything from that person) I was presented with an empty page. Is this a good choice, or should I also see archived mails from that sender? But if I do, that probably means that selecting that sender should give me a list of my most recent mails from that sender regardless of what folder they are in (except perhaps deleted/junk) - I can see the sense in that, but is it what others would want, or would most prefer only to see stuff in the inbox?
So yeah, sorry that I'm asking questions more than making suggestions, but since you want to find what works most easily for most people then I think that's probably best as I don't know how "typical" I am (except that I know I have more tolerance for complex UIs than the typical smartphone user, so in that respect I'm not typical).
In the process of this I also discovered that I can reveal the nav bar by swiping from the left-hand edge (while swiping right but not starting at the edge brings up the message selection options). That I like, as it means I don't have to reach to the top of the screen to bring the nav bar up, but I don't know how to make it more discoverable (unless the initial documentation would have told me - I never read that stuff!).
P.S. I noticed that the new options are only available in the free version so far, so currently have both so that I can test this!