The problem is exactly the same as described here - https://stackoverflow.com/questions/52484814/oracle-sql-developer-problem-initializing-welcome-page
Indeed, the Open JDK was installed. I installed Oracle Java 8 JDK, chose a new version of java after that, checked the environment variables, but still the problem remained - sql developer runs with the same error - Problem initializing the JavaFX runtime. This features requires JavaFX. Tell me, who knows, please, what have I missed?