This script helps you to link Data Sources to SSRS after a migration to a different report Report Server.

linking-data-sources-ssrs-reports.ps1

$TargetReportServerURL = "http://MySSRSServer/ReportServer"
$ReportServer = "MySqlServerInstance"
$ReportServerDB = "ReportServer"
$RootFolder = "/MyReports"
$DataSourceUrlPath = "/MyReports/Data Sources/SalesDataSource"

<#
This query assumes that in the $RootFolder you have reports that links to only a single Data Source.
If you have in the same $RootFolder reports that have different data sources, you would a new parameter 
   and also change your WHERE clause to add this possibility.
#>
$Reports = Invoke-sqlcmd2 -ServerInstance $ReportServer -Database $ReportServerDB -Query "SELECT C.Name AS report_name,
       DS.Name AS data_source_name,
       PARENT.Path + '/' + C.Name AS full_report_url
FROM dbo.Catalog C
    INNER JOIN dbo.Catalog PARENT
        ON PARENT.ItemID = C.ParentID
    INNER JOIN dbo.DataSource DS
        ON C.ItemID = DS.ItemID
    LEFT OUTER JOIN dbo.DataSets DSET
        ON DSET.LinkID = C.ItemID
    LEFT OUTER JOIN dbo.DataSource DSET_SRC
        ON DSET_SRC.ItemID = DSET.ItemID
WHERE C.Type = 2
      AND PARENT.Path LIKE '$RootFolder%';"

foreach ($report in $Reports) {
    try {
        $FormatedReport = $report.full_report_url
        $data_source = $report.data_source_name
        Set-RsDataSourceReference -ReportServerUri $TargetReportServerURL -Path $FormatedReport  -DataSourceName $data_source -DataSourcePath $DataSourceUrlPath -Verbose
    }
    catch {
        return $FormatedReport
    }
}