In a manner characteristic of carousing; in a way that involves lively, boisterous celebration and drinking.
From carousing (present participle of carouse) plus the adverbial suffix -ly, which converts adjectives and other words into adverbs describing how something is done.
This is one of those wonderfully specific Victorian adverbs that barely survives in modern English—it's the linguistic equivalent of monocles and top hats, perfectly describing a very particular kind of cheerful excess!
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