Yesh, but all the non-temple items went to rebuilding.
Next chapter or so, Ezra is berating people for building up nice houses while the Temple was in disaster. They ran out quick.
And so it all remained for several hundred years. (It functioned, but it took quite some time before it as properly redone.)
Thank you for pointing out that grumpy was referring to King Solomon’s wealth and I was relating to the Temple’s instruments of worship. Those were on my mind and I erred. They are not the same. The Temple items were returned, but what account is there of Solomon’s wealth?
Solomon passed to his fathers around 935 to 921 BC depending on who is reporting and eventually his sons went on to rule both North (Israel/Ephraim) and South (Judah) Israel so it seems his wealth did not go to Babylon. At least not only to Babylon as the Assyrians took Northern Israel around 740 BC while Southern Israel was taken by Babylon in 586 BC. So you have to consider where Solomon’s wealth went between his death and the fall of Southern Israel.
Please re-check Ezra and Nehemiah’s account along with other accounts in the Torah. Again, your recollections of the event may differ.