YouTrack can only be integrated as a task provider. This is not like the Atlassians IDE-Connector, which allows you to completely solve the problem with the IDE.
Also note that when you connect YouTrack as the default task provider, you will see only open tasks assigned to you. Therefore, you must first go to the YouTrack website and ask you a question, then it will appear in IDEA.
Unlike using JIRA as a task provider, it will not provide you with a list of tasks; you will have to search by the full task identifier to display it.
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