"Adding to the carpet of flowers outside the cathedral" is called an adverbial present participle.
An adverbial participle comes from an adverbial dependent clause.
Subject(main) + Verb(main) CONJUNCTION subject + verb.
--> Subject(main) + Verb(main) verb+ing.
However, when we change the dependent clause into a participle, before we take out the subject in the dependent clause and put that -ing after the verb, we must check that both subjects are the same.
Thus, we can safely rewrite your sentence like the below:
As the day drew to a close, Norwegians continued to pay their tribute to the dead as they added to the carpet of flowers outside the cathedral.
So, this is how I would translate/understand the sentence: Norwegians continued to pay their tribute to the dead as they "filled" the carpet of flowers outside the cathedral.