No, there is no such option in phpstorm.
You can export only individual tables from the database by clicking ONE separate table (does not work if you select several tables) and open the mouse menu (right music). There you select "Save to file ..." a Select what you need (for example, "SQL Insert Statement").
To have a good DB-Client for managing all Material, use DBeaver (stand-alone version) or MysqlWorkbench. I prefer DBeaver.
suther
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