This is a policy change made in December 2022.
SkyClub Access Policy Changes (Dec 2022 Announcement)
It’s confusing, but basically for DL GM or higher, just traveling internationally doesn’t get you get access to the SkyClub anymore (though you can still access other skyteam lounges, such as if you’re connecting in CDG or AMS ). You need to be in PS or D1 for the SkyClub (or flying in domestic first to Canada/Mexico/Central America).
People with SkyTeam Elite+ status from a partner airline are not subject to the PS/D1 restriction on international itineraries.