C. F. Keil and Franz Delitzsch on Ezra 1:4

Ezr 1:4 וגו וכל־הנּשׁאר are all belonging to the people of God in the provinces of Babylon, all the captives still living: comp. Neh 1:2.; Hagg. Ezr 2:3. These words stand first in an absolute sense, and וגו מכּל־מּקמות belongs to what follows: In all places where he (i.e., each man) sojourneth, let the men of his place help him with gold, etc. The men of his place are the non-Israelite inhabitants of the place. נשּׂא, to assist, like 1Ki 9:1. רכוּשׁ specified, besides gold, silver, and cattle, means moveable, various kinds. עם־הנּדבה, with, besides the free-will offering, i.e., as well as the same, and is therefore supplied in Ezr 1:6 by על לבד. Free-will offerings for the temple might also be gold, silver, and vessels: comp. Ezr 8:28; Exo 35:21.