Even the inhabitants of Jerusalem of that time would not have been as familiar with the night sky as eastern astrologers. Something that might not be all that obvious as something unusual, would look quite " out of place" to those who really studied the night sky".
As far as the "star" remaining stationary over Bethlehem, I suspect that is a little literary license, or misunderstanding of the way such events are spoken of, and whatever it was merely appeared in the same place relative to the other stars for a long time, which I tend to think discredits the conjunction hypothesis, especially involving Venus. Jupiter and/or Saturn and a "background star", perhaps.
IMO, the Magi had been taught the prophesies and secrets of the stars by Daniel.
The magi held faithful to these teachings until they began following celestial events and then saw the sign for the birth of the new king.
The Magi journeyed to Bethlehem and found the small child (not a baby)there.
This caravan has to be larger than three guys on camels as the Magi were dignitaries in their own land and were carrying gifts fit for a king, not token gifts.
Herod was surprised and outraged.
The Magi were warned and left.
Joseph and Mary were warned and left.
Herod killed the males 2 and under giving more evidence that Jesus wasn’t simply an newborn infant.