Difficult to find which distribution group was assigned to which shared mailbox

VasilMichev We have hybrid Exchange and basically used synced AD accounts and synced on-premise distributiongroups (delegation groups) for the shared mailbox setup. When the shared mailbox and its AD account deactivated the associate distribution groups or named delegation groups remained and were not deactivated as the shared mailbox. These delegation groups are what I call or named stale delegation groups and there are hundred.
My basic problem I would need to write a powershell script which one by one goes through the existing synced groups and examines whether there is a corresponding live shared mailbox.
So I would need the complete invers method of the "Get-MailboxPermission "primarysmtpaddress" | where {(($_.IsInherited -eq $false) -and ($_.AccessRights -like "*FullAccess*") -and ($_.User -notlike "NT Authority\SELF") -and ($_.Deny -eq $false))} | select -expand User" and "Get-RecipientPermission "primarysmtpaddress" | where {(($_.IsInherited -eq $false) -and ($_.AccessRights -like "*SendAs*") -and ($_.Trustee -notlike 'NT Authority\SELF') -and ($_.AccessControlType -eq 'Allow'))} | select -expand Trustee" powershell query. Actually I need a powershell query where the input should be the primarysmtp address of the delagation group.