Multiple Email Addresses - User Navigation
UPDATE: Now both my email addresses have switched to the new UI and I am still not able to navigate between the two accounts. I am very disappointed, this is an incredibly sloppy way to introduce your users to a new UI. This seems to be unfinished - you should have allowed your users to opt-in at will if they wanted to be a part of experimental, sloppy changes.
I have 2 Yahoo email addresses. One of them (without my permission) was switched over to the new Yahoo UI, which I do not approve of. I was able to switch my account to "Basic Mail", which I also do not approve of as the "Basic Mail" has no user settings, though it is better than the new "Standard" UI. I am very happy to see that my other account is still on the UI that I had set it to. THAT SAID, when I am logged into the New UI Account, I am unable to switch to my other inbox without going to a new page. This is a terrible user experience. I stayed on Yahoo Mail for years without switching to Gmail because I thought Yahoo better allowed me to organize and view all my messages at a high level without any flashy features getting in the way. I am very sad that Yahoo has decided to make the decision to be more like Gmail, but furthermore, if I am not able to switch between my two inboxes with one click of a button on the same page, I will be sure to delete both accounts.

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"you should have allowed your users to opt-in at will if they wanted to be a part of experimental, sloppy changes."
Hi Grace, we actually did! Since last June, there was a button in the top, right hand side where you could opt in and out of the new experience. That way we could gather feedback and keep improving the new experience. It's now come where we need to start transitioning everyone to the new desktop.
Gmail - You mention it looks like Gmail. We are assuming you are referring to the Inbox Categories at the top of your Inbox. Yes, this is new! But of course we know not everyone would want or need this therefore you can disable Inbox Categories under Settings and go back to having just one Inbox. Just go to Settings > Personalize Inbox and toggle off Inbox Categories.