Apparently, I've found a solution of the problem. Actually not a real solution, just a tricky workaround.
I have Microsoft 365 Business Basic Plan and wanted to try New Outlook, but got the same error message as topic starter did. I wrote to Microsoft Support and quite quickly got the answer. They said:
"…please be informed, that the Microsoft 365 Business Basic plan provides access to the Web and mobile versions of Outlook. Unfortunately, the desktop version of Outlook for Windows is not included in this plan. To illustrate, I have attached a screenshot below for your reference."

Of course I wasn't satisfied with the answer because I'm not going to use Office 365 Desktop Applications, I only want to use FREE New Outlook application as a mail client to access my Exchange mailbox the same way like I do that with Mail & Calendar for Windows. I thoroughly explained my standpoint in reply to Microsoft Support and now waiting for their answer.
As a temporary workaround I bought Microsoft 365 Business Standard subscription for a month and (surprise!) I managed to add my Microsoft Business mailbox to New Outlook. After that I canceled new subscription and assigned back my old Microsoft Basic plan. Application works fine.
New Outlook checks subscription type only once before adding account and keeps that information in folder:
<username>\AppData\Local\Microsoft\Olk\EBWebView\Default\Local Storage\leveldb
After adding all accounts to New Outlook I saved a copy of that folder just in case. Even after reinstalling New Outlook it's enough to replace that folder and all accounts are restored.
It's a temporary solution but hope it could be helpful for someone too.