The symbol of the Babylonian yoke plays a major role in Jeremiah's ministry. In some verses it symbolizes obedience to God but in the later chapters it refers to the yoke of the Babylonian ruler. In the case of vs. 30:8, "his" is the right translation.
In Jer. 2 and 5, the yoke indeed belongs to God.
Know then, and see, how evil and bitter
is your forsaking the Lord, your God, And your showing no fear of me,
oracle of the Lord, the God of hosts. 20 Long ago you broke your yoke,
you tore off your bonds.
You said, “I will not serve." (2:19-20)
Let me go to the leaders
and speak with them; For they must know the way of the Lord,
the justice of their God. But, one and all, they have broken the yoke,
torn off the harness. (5:5)
But starting in Jer. 27, the yoke symbolizes subservience to the king of Babylon:
The Lord said to me: Make for yourself thongs and yoke bars and put
them on your shoulders. 3 Send them to the kings of Edom, Moab, the
Ammonites, Tyre, and Sidon, through the ambassadors who have come to
Jerusalem to Zedekiah, king of Judah, 4 and command them to tell their
lords: Thus says the Lord of hosts, the God of Israel, Thus shall you
say to your lords... Now I have given all these lands into the hand
of Nebuchadnezzar, king of Babylon, my servant; even the wild animals
I have given him to serve him.
In chapter 28 Hananiah the [false] prophet, breaks the yoke that Jeremiah has made and says, in the Lord's name:
3 Within two years I will restore to this place all the vessels of the
house of the Lord which Nebuchadnezzar, king of Babylon, took from
this place and carried away to Babylon.
Jeremiah at first seems to accept Hananiah's prophecy but soon receives another revelation from God:
Go tell Hananiah this: Thus says the Lord: By breaking a wooden yoke
bar, you make an iron yoke! 14 For thus says the Lord of hosts, the
God of Israel: A yoke of iron I have placed on the necks of all these
nations serving Nebuchadnezzar, king of Babylon, and they shall serve
him; even the wild animals I have given him.
Finally, in chapter 30, Jeremiah pronounces the words of hope, that once the price has been paid through their Exile, the people of Judah will be freed and the David kingship will be restored.
the days are coming—oracle of the Lord—when I will restore the fortunes of my people Israel and Judah ...Ah! How mighty is that day—
there is none like it! A time of distress for Jacob,
though he shall be saved from it. 8 On that day—oracle of the Lord of hosts—I will break his yoke off your neck and snap your bonds.
Strangers shall no longer enslave them; 9 instead, they shall serve
the Lord, their God, and David, their king, whom I will raise up for
Conclusion: although in the beginning of his book, Jeremiah speaks of God's yoke, in chapters 27-30 the yoke symbolizes the oppression of the king of Babylon. This also applies to the prophecy mentioned in the OP, in which God promises both liberation from Babylonian oppression and the re-establishment of the Davidic kingdship.