The wording of your question suggests that manner adverbs are somehow more normal or central than other sorts of adverb. I see no reason to think that is true. There are at least three theories about the syntactic types of adverbs:

• containing constituent (see [Thomason & Stalnaker][1] and also Zeno Vendler), where manner adverbs are taken to be within verb phrases
• modified constituent (see [McCawley, chapter 19][2]), where manner adverbs are taken to modify verb phrases
• grammatical relation (see [me][3]), where manner adverbs are taken to have the same grammatical relation as direct objects

In all three theories, there are other types of adverbs as well, and manner adverbs do not have a special privileged status. Also, in all three, the same -ly word can sometimes have several different interpretations, depending on the type of adverb it is. [1]: https://www.jstor.org/stable/4177764?seq=1#page_scan_tab_contents [2]: https://books.google.com/books?id=k6-C5AWWqjQC&q=domain%20adverb#v=snippet&q=domain%20adverb&f=false [3]: https://linguistics.stackexchange.com/questions/17271/how-can-psg-describe-the-vertical-dimension-of-sentence-structure

The wording of your question suggests that manner adverbs are somehow more normal or central than other sorts of adverb. I see no reason to think that is true. There are at least three theories about the syntactic types of adverbs:

• containing constituent (see Thomason & Stalnaker and also Zeno Vendler), where manner adverbs are taken to be within verb phrases
• modified constituent (see McCawley, chapter 19), where manner adverbs are taken to modify verb phrases
• grammatical relation (see me), where manner adverbs are taken to have the same grammatical relation as direct objects

In all three theories, there are other types of adverbs as well, and manner adverbs do not have a special privileged status. Also, in all three, the same -ly word can sometimes have several different interpretations, depending on the type of adverb it is.