As always, there's plenty more to be said, but u/lcnielsen has answered many related questions. Particularly you might be interested in how Zoroastrianism influenced Judaism, how it influenced Christianity, and the use of "Zoroastrian" to describe Achaemenid kings.
The only detail I'd add, just because you asked about Cyrus specifically, is his own famous influence on Judaism/the Jews. Cyrus was the one who ended the Babylonian Exile and first allowed the Jews living in Babylon to return to Judea. For that act, he earned himself a noteworthy place in Biblical history as the only non-Jew to be called a messiah (usually translated to anointed in the Christian Old Testament). Of course, not many Jews seem to have actually taken him up on that offer, with much more of the exile population returning after the reign of Darius I. Ultimately this has very little bearing on actual theology. The important part is that someone ended the exile regardless of who that was specifically, but obviously it is an important moment in Jewish history.