Outlook only syncs an IMAP account if the Inbox\Inbox folder is active. How to fix?

Question

IMAP

2 weeks ago I caught a glitch on Windows Server 2019 - MS Outlook 2016 stopped correctly synchronizing mail via IMAP from a Linux server (Dovecot+Exim). The following happens: we throw a letter on our mailbox (from anywhere), we wait. Next is some magic. If the cursor is on the Inbox folder, the mail arrives immediately. If any other folder is active, for example, Deleted or Sent, the letter does not arrive no matter how much you wait for it. The timer does not always even work in the "Sending / Receiving" settings, where the standard 30 minutes can be changed. Next, click on the Inbox folder and all letters immediately arrive.

Tried:
Delete Outlook profile,
Delete and re-create accounts,
Disable add-ons by policy,
Scanpst, Firewalls
,
Antiviruses,
Rollback to Outlook 2013,
Office reinstallation,
Windows clean user profile,
MS package troubleshooting tool,
Rollback of September updates: system and Office,
set Inbox as the root folder,
Selected folders for synchronization in send/receive settings.

None of the above helped.

At first I thought that the problem was in the mail server on Linux, but there were no updates, the configuration did not change. Then, perhaps, the problem is with Windows Server, where Outlook is installed, but I reproduced exactly the same garbage on my home Windows 10 + MS Office 2016.
Accurate to a comma, moreover, with Yandex and Google servers.

I asked my friends to check their Outlook behavior - the same thing. If a folder other than the Inbox is active, no emails will be received.
Other programs, for example, Thunderbird from Mozilla, work like clockwork: I threw a letter - it came right away. Even Outlook mobile works fine.

The problem is not observed on Outlook 2010, but it is already old.

Someone writes that it is necessary to find letters larger than 25MB (Outlook has a limit on the size of the letter) in the Inbox folder and delete it - it does not help.