Institutional logins should work — which is why it's trying to import at all. But if it's getting 0 items, that really just means it's not finding any data.

To confirm, if you do that login process outside of Zotero, do you actually see your Mendeley data?

Hi, I managed to get it working. I'll let you know what I discovered in case it is useful for future troubleshooting.

Before Elsevier moved to a 'one-login-everywhere' system, I had my personal email account linked to Mendeley, and my Scopus/Elsevier account linked to my university email address. At some point during the shift to a 'one-login-everywhere' system, my institution got linked to my personal Mendeley account. So, based on this situation, I would be able to go to the Mendeley website and login directly through my personal email address, or select 'Login via institution', which would take me to my institutions' interface to log in using my institutional email and password. Whichever way I logged in, I would be on the same Mendeley account -- the one linked to my personal email.

When trying to import Mendeley library into Zotero, ideally I would have just logged in via my personal email address. Of course, that doesn't work because Elsevier requires me to validate via email on an external browser (as noted in my initial post above). But I was able to log in via my institutional account -- which, via Mendeley's website, would still take me to my Mendeley account linked to my personal email. As mentioned, when trying this, the import would 'complete' with nothing imported.

So I tried something else: I logged into Mendeley using my institutional email and a password linked to Scopus/Elsevier kept from before it became a 'one-login-everywhere' system. Note that this is different to 'Login via institution'. I am using my institutional email to log in, but not via my institutions' interface. Once logged into Mendeley, it was a completely different account -- linked to my institutional email, and with nothing in my library. This is obviously what Zotero was picking up when coming to import.

The way I resolved it likely isn't available to everyone... My aforementioned institutional account was from somewhere I left 5 years ago (but still maintain ties as an honorary member). I've since joined a new institution. So, I linked my new institution -- which at present is not linked to any of Elsevier's systems because I've erstwhile maintained my old institution's access -- to my Mendeley account linked to my personal email.

When trying to import into Zotero using the NEW institution, it worked and imported all 9gig/4400 entries. Unlike the old institution, it would not have been confused by an institutional email linked to another Elsevier service prior to their 'one-login-everywhere' system.

TLDR: It's an issue at Elsevier's end and the carnage of having a 'one-login-for-everywhere' where, prior to that, some accounts were based on an institutional email, and others were based on a personal email -- and then 'wrapping it all' with an institutional link. I hope this makes sense?

@pdenno: You'll need to get help from Elsevier. Even if we found a way to support logins that triggered email confirmation (e.g., by pasting in the link from the email), that presumably wouldn't help you, if you can't access the institutional account.