The repeated use of "sons" is also significant. The move from being servants to sons is a big deal.
"So you are no longer a slave, but a son, and if a son, then an heir through God." Gal. 4:7
"For all who are eled by the Spirit of God are sons of God. For you did not receive the spirit of slavery to fall back into fear, but you have received the Spirit of adoption as sons, by whom we cry, “Abba! Father!” Rom. 8:14-15
The liberty is kingly. Christ's obedience as our High Priest led to His exaltation and He shared that with the Firstfruits Church (which Church is the context here). If Adam had obeyed the Law he would have enjoyed the liberty of the glory of God by entering into His rest, but he chose slavery and became a servant.
The liberty of a king is his submission to God's Law as his light. He becomes the Law incarnate by the Spirit. The "trainer wheels" of the childhood of the Law become redundant. The ministry of angels (those who administered the Old Covenant as our guardians) is finished, which is what we see in the Revelation - one by one, the angels carry out their final missions and leave the heavenly sanctuary empty, ready for the OC saints and NC apostles to enter and be enthroned as a new government. Those who were previously under the flaming sword (Adam/Passover) are now qualified to bear it as God's representatives.
So, basically, the freedom of the glory is the liberty of judicial maturity. The Father gave the "car keys" to the first qualified Son, and He includes us in His government by His Spirit.