Get the TeamsMessagesDataFolder

gistfile1.txt

$folderid= new-object Microsoft.Exchange.WebServices.Data.FolderId([Microsoft.Exchange.WebServices.Data.WellKnownFolderName]::Inbox,$MailboxName)   
$TeamsMessagesDataFolderEntryId = new-object Microsoft.Exchange.WebServices.Data.ExtendedPropertyDefinition([System.Guid]::Parse("{E49D64DA-9F3B-41AC-9684-C6E01F30CDFA}"), "TeamsMessagesDataFolderEntryId", [Microsoft.Exchange.WebServices.Data.MapiPropertyType]::Binary);
$psPropset= new-object Microsoft.Exchange.WebServices.Data.PropertySet([Microsoft.Exchange.WebServices.Data.BasePropertySet]::FirstClassProperties) 
$psPropset.Add($TeamsMessagesDataFolderEntryId)
$RootFolder = [Microsoft.Exchange.WebServices.Data.Folder]::Bind($service,$folderid,$psPropset)        
if ($RootFolder.TryGetProperty($TeamsMessagesDataFolderEntryId,[ref]$FolderIdVal))
{
     $TeamsMessagesFolderId= new-object Microsoft.Exchange.WebServices.Data.FolderId((ConvertId -HexId ([System.BitConverter]::ToString($FolderIdVal).Replace("-","")) -service $service))
     $TeamsMessagesDataFolder = [Microsoft.Exchange.WebServices.Data.Folder]::Bind($service,$TeamsMessagesFolderId);
}       
        
function ConvertId{    
    param (
            [Parameter(Position=1, Mandatory=$false)] [String]$HexId,
            [Parameter(Position=2, Mandatory=$false)] [Microsoft.Exchange.WebServices.Data.ExchangeService]$service
       )
    process{
        $aiItem = New-Object Microsoft.Exchange.WebServices.Data.AlternateId      
        $aiItem.Mailbox = $MailboxName      
        $aiItem.UniqueId = $HexId   
        $aiItem.Format = [Microsoft.Exchange.WebServices.Data.IdFormat]::HexEntryId      
        $convertedId = $service.ConvertId($aiItem, [Microsoft.Exchange.WebServices.Data.IdFormat]::EwsId) 
     return $convertedId.UniqueId
    }
   }

Did you try to add Full Permissions via add-mailboxpermission ? the other thing would be try to retrieve it via code instead it could just be a bug in that app