Some more information:
In the akonadi console I can see an error message when accessing the inbox: Unsupported type
When I login via CLI I get this information when accessing the inbox folder:
* OK [CAPABILITY IMAP4rev1 XLIST SPECIAL-USE UNSELECT UIDPLUS IDLE LITERAL+ LITERAL- AUTH=LOGIN] Service ready
A capability
* CAPABILITY IMAP4rev1 XLIST SPECIAL-USE UNSELECT UIDPLUS IDLE LITERAL+ LITERAL- AUTH=LOGIN
A OK CAPABILITY completed
A status INBOX (messages)
* STATUS "INBOX" (MESSAGES 1832)
A OK STATUS completed
So in general it seems to work, but kmail is not working with this inbox, but the access to other provider mailbox (eg. gmail) with imap is still working, so it seems not to be a general imap problem with kmail.
Strange ....