According to Google Gemini, at its core, agathos conveys the idea of something being morally excellent, beneficial, or desirable. It encompasses both intrinsic goodness and external qualities that contribute to value.
The meaning of "work together for good" is simple here, but the assertion is profound. It points to the omnipotence and omniscience and providence of the Creator. All things means everything -- events, circumstances, good or evil, big or small -- God is actively causing all things to work together for His will and His purposes for the benefit of a group of people, namely "those who love God, to those who are called according to His purpose."
The agathon is plainly good for certain people, not just for God. People who love God and are called according to His purpose may have various ideas about what is good. But in any case the action of causing all things to work together for good is clearly being done by God. The good here is the result of God's supernatural, active, intentional, elaborate orchestration. So the result of God's providential work must be understood as good by God's definition, that is, what God considers to be good.
Later in the same letter, the NASB translates the same word agathon as "for good" in Romans 13:4 referring to submission to rulers "for [the ruling authority] is a servant of God to you for good." Note again that the ruling authority-- in this case, the authority over the Romans to whom Paul was writing -- was a servant of God whether they knew it or not. This again points to the omnipotence and omniscience and providence of the Creator. Governments, rulers, armies, forces, laws, tribunals -- all of these -- are among the "all things" which God causes to "work together for good to those who love God, to those who are called according to His purpose." (Rom 8:28)