You would need to name the dictionary for us to be sure, but I imagine you are correct, because the word “verbose” does indeed have negative connotations. Here’s the definition in the MacMillan: “using more words than necessary, and therefore long and boring”

Verbose is generally understood to mean. Using too many words and thus becoming tiresome or boring. To the listener, who may disapprove. I have found synonyms for verbose that suggest you can apply disapproving to verbose. But it is not a generally understood synonym for verbose. You need to supply a link to the dictionary. Verbose Synonyms. https://www.thesaurus.com/browse/verbose?s=t repetitious, gabby, talkative, tautologous, etc. all mean too wordy. However finding a synonym in the other direction was not as successful.. Disapproving synonyms were more difficult to find that also matched the other synonyms for verbose.

I'm confused about that too and I'm a native speaker. It generally means too "wordy", too many words, or an unnecessary amount of words. Just stay with that general definition.