Csproj/Vbproj file addition

<ItemGroup>
  <EmbeddedResource Include="..\DatabaseProjectName\$(OutputPath)\DatabaseProjectName_Package.sql">
    <Link>DatabaseProjectName_Package.sql</Link>
  </EmbeddedResource>
</ItemGroup> 

C# migrate db method

private static void MigrateDatabase(string connectionString, string sqlPackageResourceName)
{
    string databaseName = (new System.Data.SqlClient.SqlConnectionStringBuilder(connectionString)).InitialCatalog;
    using (var sqlConnection = new System.Data.SqlClient.SqlConnection(connectionString))
    {
        sqlConnection.Open();
        using (var sqlRunner = new com.rusanu.DBUtil.SqlCmd(sqlConnection))
        {
            sqlRunner.Environment.Variables.Add("DatabaseName", databaseName);
            sqlRunner.Executing += (object sender, com.rusanu.DBUtil.SqlCmdExecutingEventArgs e) => Console.Write(".");
            var assembly = System.Reflection.Assembly.GetExecutingAssembly();
            using (var sqlPackageStream = assembly.GetManifestResourceStream(assembly.EntryPoint.DeclaringType.Namespace + "." + sqlPackageResourceName))
            {
                Console.Write("Bringing the \"" + databaseName + "\" database up-to-date by running any pending migrations");
                if (!sqlRunner.ExecuteStream(sqlPackageStream))
                    throw new Exception("Database deployment failed. SQL Server error details: " + sqlRunner.LastException.Message + ", Batch that raised error: " + sqlRunner.LastBatch);
                Console.WriteLine("done");
            }
        }
    }
}

C# call to migrate method

const string ConnectionString = @"Data Source=(localdb)\ProjectsV13;Integrated Security=True;Pooling=False;Connect Timeout=30;Initial catalog=AdventureWorksAzure_Embedded";
const string SqlPackageResourceName = @"AdventureWorksAzure_Package.sql";

static void Main(string[] args)
{
    // Deploy the database from the embedded resource to the specified connection or incrementally migrating it to the latest state
    MigrateDatabase(connectionString: ConnectionString, sqlPackageResourceName: SqlPackageResourceName);
    Console.WriteLine("Press any key to exit");
    Console.ReadKey();
}

C# Methods to trim connection string

private static string GetConnectionStringWithoutInitCatalog(string connectionString, out string databaseName)
{
    var connStringBuilder = new SqlConnectionStringBuilder(connectionString);
    databaseName = connStringBuilder.InitialCatalog;
    if (string.IsNullOrWhiteSpace(databaseName))
        throw new Exception("Could not find initial catalog attribute in connection string.");
    connStringBuilder.InitialCatalog = ""; // We remove the "Initial Catalog" attribute because the database may not exist yet
    return connStringBuilder.ToString();
}
private static bool DoesDatabaseExist(string connectionStringNoInitCatalog, string databaseName)
{
    using (var conn = new SqlConnection(connectionStringNoInitCatalog))
    {
        conn.Open();
        using (var cmd = new SqlCommand("select count(*) from sys.databases where name = @p1", conn))
        {
            cmd.Parameters.Add("@p1", SqlDbType.NVarChar).Value = databaseName;
            return Convert.ToInt32(cmd.ExecuteScalar()) != 0;
        }
    }
}

C# Trim database name from connection string

private static void MigrateDatabase(string connectionString, string sqlPackageResourceName)
{
    string databaseName;
    string connStringNoDatabaseName = GetConnectionStringWithoutInitCatalog(connectionString, out databaseName);
    // If database doesn't exist yet, then connect to the default db (usually [master]) instead of the specified db,
    // in order to allow the  SQL Change Automation migration package to create the db first.
    // NOTE: For Azure SQL deployments, the first deployment will fail after the db is created. Re-run the deployment to migrate the db
    if (!DoesDatabaseExist(connStringNoDatabaseName, databaseName)) 
        connectionString = connStringNoDatabaseName;
    using (var sqlConnection = new SqlConnection(connectionString))
    {
       sqlConnection.Open();
        using (var sqlRunner = new com.rusanu.DBUtil.SqlCmd(sqlConnection))
        {
            sqlRunner.Environment.Variables.Add("DatabaseName", databaseName);
            sqlRunner.Executing += (object sender, com.rusanu.DBUtil.SqlCmdExecutingEventArgs e) => Console.Write(".");
            var assembly = System.Reflection.Assembly.GetExecutingAssembly();
            using (var sqlPackageStream = assembly.GetManifestResourceStream(assembly.EntryPoint.DeclaringType.Namespace + "." + sqlPackageResourceName))
            {
                Console.Write("Bringing the \"" + databaseName + "\" database up-to-date by running any pending migrations");
                if (!sqlRunner.ExecuteStream(sqlPackageStream))
                    throw new Exception("Database deployment failed. SQL Server error details: " + sqlRunner.LastException.Message + ", Batch that raised error: " + sqlRunner.LastBatch);
                Console.WriteLine("done");
            }
        }
    }
}