Why did apostle Paul connect Hagar with Sinai and Jerusalem in Galatians 4? Was it to free believers in Yeshua (Jesus) as God’s Messiah from obedience to God’s Law?

Why did apostle Paul connect Hagar with Sinai and Jerusalem in Galatians 4? Was it to free believers in Yeshua (Jesus) as God’s Messiah from obedience to God’s Law?
Abraham obeyed God and had himself and all the men in his household circumcised and they all agreed to do it, including Ishmael. In the flesh, there’s no reason for circumcision, but if you believe in God, there’s every reason for it. Actively trusting God’s words — called “faith” and “belief” — is what makes one righteous.
Taking a closer look at 1st Kings 2, we see a pattern of The Adversary (haSatan) and anti-Messiah revealed by two men in Scripture who lead parallel lives more than 1,000 years apart.
In part three of a study on Genesis 21, we read about the confrontation between the ruler Abimelech and Abraham. Meanwhile, Ishmael grows up and becomes a problem in Abraham’s household, so Abraham sends him and his mother away.
Genesis 21 has close parallels with apostle Paul’s illustration in Galatians 3-4 on the “son of the promise” from the “free woman” and the “son of the flesh” from the slave woman.
Genesis 21 has close parallels with apostle Paul’s illustration in Galatians 4 on the “son of the promise” from the “free woman” and the “son of the flesh” from the slave woman.
This chapter is our introduction to Hagar, Sarai’s Egyptian maidservant. We see how Hagar was exalted and then brought down. When Hagar fled and was at her lowest point, we discover God had His eyes on Hagar and had a purpose for her and her unborn son.