How was the sending of prophets by God, both constructive and in line with the keeping of the covenant
This is a great question. Let me make three points.
First, God's covenant was to bless the people in so far as they obeyed. We see this pattern in the covenant made with Moses and the Israelites at Sinai. We also see this in the whole book of Deuteronomy, as the book is in the form of a covenant with God. We also see this played out in the books of 1 and 2 Kings and 1 and 2 Chronicles. In short, will the kings obey or not?
Second, by sending prophets, God is in essence saying to the Israelites that they need to come back to their senses. They need to obey the covenant and stop following false gods and idols, to use the language of the prophets.
Third, all of this is constructive, because God is sending reminders and warnings. He is telling his people that continued disobedience will lead to exile and destruction and obedience will lead to restoration and life. We see this pattern in almost every prophet.