As is often the case, I am mystified by the JPS translation in Jer 31:34. The two words we should "heed" are:
- יָדַע (yada) = "to know". The JPS translation "heed" is quite interpretive.
- יְהוָ֑ה (YHWH) = the tetragammaton, "The LORD". It is not the word "G_d" nor "me".
Hence the twice occurring phrase in Jer 31:34 is, "know the LORD".
The prophet's teaching in Jer 31:34 is rather simple and uncomplicated - the passage prophesies of a time (then still future) when teaching about "the LORD" will be unnecessary, "because they will all know Me, from the least of them to the greatest, declares the LORD."
Concomitantly with this time, the prophecy also predicts that, "after those days, the LORD, I will put My law [Lit: Torah] in their minds and inscribe it on their hearts. And I will be their God, and they will be My people." Jer 31:33. Thus, the "they" and "them" are God's covenant people, committed Christians now.
This is referring to the "New Covenant", V31, as confirmed in Heb 8:7-12 and Heb 10:15-17. Thus, the "they" and "them" are God's covenant people, committed Christians now. This will ultimately be fulfilled when, as described by Paul in 1 Cor 13:12 -
Now we see but a dim reflection as in a mirror; then we shall see face
to face. Now I know in part; then I shall know fully, even as I am
fully known.
... and also by John in Rev 22:4 -
They will see His face, and His name will be on their foreheads.