Did Prophet Sulaiman threaten Queen Bilqis to accept the one True God otherwise he would overrun or conquer her country? How do we reconcile with the fact that there is no compulsion in religion?

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Her people did not worship the one God. They were polytheists spreading false beliefs, so Prophet Sulayman made it clear to them that if they continue spreading their false/corrupt beliefs and practices then he will conquer them. Prophet Sulayman was a prophet who was also a king/ruler, and he was instructed by God to stop the false beliefs of other nations. So his rule was more of an exception.