Hi Przemek!
The possible reason for documents not synchronizing is the permissions set in Sharepoint Online.
There is this part in documentation that is important to note:
Please note that SharePoint Online is nuanced and has a limitation.
SharePoint Online has the concept of a "Members" group that SharePoint Online manages itself. The API endpoints for the "Visitors" and "Owners" groups within their grouping system cannot be accessed via API. Therefore, if you are trying to grant access using those groups, it will not work — Workplace Search cannot understand them. We recommend creating the equivalent groups in Office 365 Groups and use that to map instead.
Could it be that documents missing in Workplace Search are only accessible to Owners or Visitors? (See more about these groups here: Sharing & permissions in the SharePoint modern experience - SharePoint in Microsoft 365 | Microsoft Learn)
By the way, do you already have a support case open with Elastic? If so, let's continue the communication there? I understand that you are trying to find the solution to this problem, but it would be much easier for anyone who takes this case if all the communication is happening in one place.