"At ease" is defining "put", so it's functioning as an adverb phrase. "About the company's future" is defining "ease", so it's functioning as an adjective phrase.

"At ease" can be interpreted as either an adjective phrase that modifies "investors" or an adverb phrase that modifies "put". The two interpretations are equally correct: 1) adjective: The expression "at ease" commonly works as an adjective. For instance, you can say "he is at ease" or "he feels at ease". In both sentences, "at ease" functions as a predicative complement, which is to say an adjective. So, putting someone "at ease" ascribes to that person an adjective. 2) adverb: In general, you "put something somewhere". So when you say the results "put the investors at ease" you are telling WHERE the results PUT them". Phrases that answer a question "where?" are adverb phrases. "About the company's future" modifies the adjective or adverb phrase "at ease". Anything that modifies an adjective or an adverb is an adverb. "About the company's future" does not describe "ease". Rather, it answers a "how?" question about the type of "at ease". Phrases that answer "how?" questions are adverb phrases.