[Source:] "More important" and "more importantly" are used as full-sentence modifiers, often in the initial position and treated parenthetically (set off with a comma). Either phrase can usually be translated as "what is more important."
More important, the armies in the east had used up all their supplies.
Many writers will use the adverb form, "importantly," thinking that the phrase
modifies a verb in the main clause; usually, however, that is not the case. The phrase will almost invariably modify, adjectivally, the entire clause, and the adjective form, "important," will suffice.
1. What's wrong with the belief that this disjunct
modifies a verb in the main clause ?
2. How does the phrase almost invariably modify, adjectivally, the entire clause? How can adjective modify an entire clause? Does this jar with the definition of an adjective?
Footnote: I already read this ELU answer,