The problem is in the following: Intellij Idea Database plugin cannot connect to Oracle database.
The reason is:
Connection to Data Source failed
java.sql.SQLException: ORA-00604: error occurred at recursive SQL level 1
ORA-12705: Cannot access NLS data files or invalid environment specified
Oracle database has some strange problems with non-english locations and languages. I need to add '-Duser.region=us -Duser.language=en' as VM args and it will resolve the problem. At least, it resolved connection problem in Tomcat.
As far as Database plugin run as a separate process, I need to add these args to database plugin's VM, but I do not know how to do it.
I tried to add this args to idea.exe.vmoptions, but it did not help.
Eventually, I need to add '-Duser.region=us -Duser.language=en' to database plugin command line or resolve the issue with connection to Oracle in another way.