There are a number of user-submitted plugins to make this happen on Classic.
At first glance, this one seems to have basic functionality: GitHub - libmanuk/SimpleOGTags: Omeka plugin to manage a simple set of Open Graph protocol tags.
It seems to be fetching item titles correctly but not media URLs (for me), so it will need some digging into the code to update. But it can get you started with generic default images and text for your site, in the meantime.
If you’re not coding-inclined, you could post an issue on the project’s github page to express interest in someone else updating the plugin.
(I tested a few others based on this code and they all seem not to work, so, don’t bother with these: GitHub - rshanrath/omeka-twitter-cards-plugin: Omeka plugin to include Twitter Card tags.)
Let me know if this is helpful and we’ll go from there.