I was having this same issue, but with actual Artboards and it was still greyed out. I finally tried Window>Asset Export, when this opens MOVE the panel somewhere else (I moved mine to the left side of the screen), otherwise it just kept closing on me as soon as I clicked on the art work to drag it. Select all "objects" or whatever you are dealing with and drag it onto the panel over the blue square in the Asset Export panel. This will create an asset for each object. Select the Format you want to save it as (PNG, JPG, SVG, PDF, or WebP). Then click on the icon to the left of Export at the bottom of the Asset Export panel to use the Export for Screens option, choose All Assets, choose where you would like to save it add any scaling you would like (I did not do this) and click Export Asset. After I did all of this I also realized I could have gone to File>Export As and THEN I would be able to click the checkbox for Use Artboards and it would have saved each one individually as well. I put both ways because I think it's always good to know more than one way to do something. This is using the latest version of AI as of 08/26/2023 on Windows 11. Hope this helps someone!