REST API doesn't return reports to new PowerBI users

Finally I have an explanation for this issue. Microsoft premium support confirmed it's expected behavior of the REST API:

REST API returns only directly shared reports with the current user and reports from installed PowerBI applications.

All the missing reports were from PowerBI applications that were not insatlled on the user account. PowerBI app installation is almost hidden feature, because all PowerBI clients from Microsoft install Power BI applications automatically when user opens a report. Unfortunately, there is no public API to install Power BI appliction. So this issue has no solution for third party apps. Workaround is only to navigate user to any Microsfot PowerBI client and install PowerBI applications by opening reports or instal them manually from marketplace.