When the Ephesians, etc, read Paul's instruction to sing, they did so with a cultural background of learning their religious terminology from the Old Testament scriptures.
When they read "sing and make melody in your hearts to the Lord", they, knowing the Old Testament scriptures much better than most of us, would realize that Paul, just as he had done twice in the previous chapter, was again alluding to scripture:
WEB Ps 108:[1 ]My heart is steadfast, God. I will sing and I will make music with my soul.
They understood the word "sing" exactly as God had taught them to understand the word "sing". You can understand the word using a non-Biblical understanding all you want, and insist that it automatically excludes instrumental music, but that is not how God taught Bible students to understand the word. Here's how he taught Bible students to understand the word "sing", and how to sing his praises to the peoples:
WEB Ps 108:[1 ]My heart is steadfast, God. I will sing and I will make music with my soul. [2 ]Wake up, harp and lyre! I will wake up the dawn. [3 ]I will give thanks to you, Yahweh, among the nations. I will sing praises to you among the peoples.