O365 Global Admin has no access to recent SharePoint Online site collections

You can use the below PowerShell script to get the details of the SPO Site Collections for the Office 365 Groups.

$cred=Get-Credential
$exchangeSession = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri "https://outlook.office365.com/powershell-liveid/" -Credential $cred -Authentication "Basic" -AllowRedirection
Import-PSSession $exchangeSession -DisableNameChecking
Connect-SPOService -Url https://tenantname-admin.sharepoint.com -credential $cred
$Groups=Get-UnifiedGroup |Where-Object {$_.SharePointSiteUrl -ne $null}
$Groups | Foreach-Object{ 
$Group = $_ 
$GName=$Group.SharePointSiteUrl
Get-SPOSite -Identity $GName -Detailed |fl
} 

To add a member to Office 365 Groups, you can use the below one.

Add-UnifiedGroupLinks -LinkType Members -Identity "engineering" -Links "alland@XXXXX.onmicrosoft.com

I am sure that the Office 365 Group's SPO File audits are available in "Audit log search" in protection centre [https://protection.office.com/#/unifiedauditlog]. Screen-shot of the audit logs for O365 groups is posted below.