How to un-cache a specific node field (also for anonymous)
You have to make sure you add #cache data inside of a render array only to render elements (containing #type, #theme or #markup). In other places of a render array it doesn't work.

Where you add cache max-age or contexts inside of an entity doesn't make a difference though, because there is no field level, only entity level caching.

Another problem is page caching for anonymous users. See How do I disable Twig and block cache for a specific module?