Figma make doesn't see my already published library

I’m struggling with the exact same scenario.

I think I get it now. It looks like Figma Make is only capable of accessing libraries published at the team level, not the organization level. If you publish at the team level, you will be able to access it. Publishing to team won’t affect your source of truth. 

Something to be advised of if your using token studio in your library, you will have to export your tokens into Figma as variables. Make is not able to tap into the 3rd party plugin.

Even if I publish a lib on team level it doesn’t show up in my make selection. The libs shown in the first screenshot are not the ones I want to see there or published myself in my org but the one I obviously published myself for my team isn’t displayed. The make File is moved to this team I published the library to, still I don’t see it and I can just see these four libs I didn’t publish. This whole make integration is still a bit wobbly considering the price point …

EDIT: Now I saw it, below the publish dialog, there is another dialog with a button “Export to Figma Make” This is obviously yes, and I overlooked it completely, but doesn’t integrate well into the library publishing mechanism really. Plus it takes ages to export the lib again.