In short: 30k users, 40k mailboxes, 100M emails and calendar entries migrated. The client is Thunderbird. The server / web side is handled by Open-Xchange, hosted by a local provider with the same name (AFAICT), which also offers commercial licensing for the otherwise-AGPL suite.
There are no high scalability improvements, it is a regular Dovecot Pro setup.
44.000 mailboxes is not really big from Dovecot Pro point of view, there are dozens of other service provider customers running six to eight digit mailbox numbers on it. Biggest European installation serves 40M mailboxes although these are consumer / SMB mailboxes which lower load provide and size compared to Schleswig-Holstein.
I don't think so. Yes, there are open source components in there. But there's also a huge amount of their own code, and can iirc present as a whole MS Exchange server to an Outlook client. There's also a user-customizable web frontend with groupware-like features. The whole package is a lot different than just combining a few packages into a bare-bones email service.
The service gets operated by Dataport AöR. Dataport is the primary service provider / datacenter of some german federal states and owned by them.
They client is mainly Open-Xchange AppSuite Web UI, some people use Thunderbird on top. There are also thousands of mobile devices, syncing via IMAP, SMTP, CalDAV, CardDAV.