Because HeidiSQL doesn't use the SQL Server Native Client(Provider = SQLNCLI11 or Provider = SQLNCLI12) to connect to SQL Server, it is not possible to connect to a LocalDB instance.
The Provider SQLOLEDB is not able to connect to a LocalDB instance.
The request is to be able to set the PROVIDER property of the connection string in HeidiSQL.
Feature request : Support for MSSQL LocalDB instance
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