Frieren: "No, you misunderstand Fern. I was going "My Digga!" As a friendly gesture."

Aura: "You can't use that word! It's our word!"

Note that the word "Digga" actually has a meaning in German which the artist wasn't aware of:

Literally a german word, she is just in touch with the youth.
https://twitter.com/Tamithewamy/status/1770086038699950411

i didn't even know that lmao
https://twitter.com/dingotoad/status/1770102537867202897

Reddit: Is Digga considered a bad/swear word in German?

Dicker can mean "big guy" in the sense of being overweight, but calling someone "dick" isn't necessarily an insult. It's just the opposite of "dünn" (thin). Calling people "fett" or "dürr" on the other hand has an insulting connotation that "dick" and "dünn" lack.

Another things to consider is that "dicker Freund" doesn't necessarily mean "fat friend", it can also mean "very good friend" in the sense that the friendship between you is thick/strong.

In practice Dicker/Digga is just "bro" and applies to guys of all body types alike. In a similar vein, Alter can be used to mean "bro", and applies to guys of all ages, not only old men.
https://www.reddit.com/r/German/comments/ggtgd2/comment/fq508lr/

Accidentally correct/non-ironic commentary right there, based on the explanation above my comment.

So you can theoretically reinterpret what's happening as Frieren expressing her breast envy, with that being the reason Fern is objecting.

Figures a leaf-lover would say that.

Bro or Buddy is Digga (in german)

This has the same energy as saying a variant of "you" in Korean or Chinese.

This is why context is important.