This is not the adverb 'beaucoup' but the expression "beaucoup de" - which Larousse refers to as a "locution déterminante", wordreference as a "preposition (of quantity)". In either case it modifies the following noun here, not the verb. So the sentence is "We drank" - (what?) - "a lot/lots of.... wine". In French that is "Nous avons bu" (or "on a bu") - (quoi ?) beaucoup de ....vin.
The adverb "beaucoup" needs to follow at the end of the passé composé of boire to modify the extent of how much was drank.
There are examples shown later in the lesson about this positioning of the adverb.
Hope this helps.
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