Both are correct points of view, but it should be noted that adverbial instead of adverb is the right word. Adverb is a word class/part of speech, while adverbial is a syntactical function. So "für alle Altersklassen" is either an adverbial in the participle clause of "geeigneter" or an attribute of the adjective "geeigneter".
The reason you have these two points of view lies in the nature of participles, which are like a mix of adjectives and verbs. They describe nouns like adjectives, but can have objects like verbs. So you can see "geeigneter" either as something more verb-like, and "für alle Altersklassen" as an adverbial, or as something more adjective-like, and "für alle Altersklassen" as an attribute. It changes nothing in the meaning and the dependency structure, it's just a different way to describe the same thing.
It is also not true that adjectives don't have such attributes, e.g. one could say
Eine für alle Altersgruppen erfreuliche Nachricht.
And "erfreulich" is not a participle.