I connected PostgreSQL to heidiSQL and each time I create a new Database, it does not appear in the database list, even after refreshing or restarting Heidi.
If I try to create it back, it tells me that the database already exists.
I really don't know what to do by now
Most probably you told your session to display only one or some of all databases:
Remove these, or add the newly created database there to let HeidiSQL display it.