Is there any connection between Birkat Hachamah and Passover?
There is no connection between the two. The timing of Birkat Hachamah is related to a solar event, whereas the Jewish calendar – and the date of Passover – is determined by the lunar orbit. Birkat Hachamah always occurs on a Wednesday morning in the beginning of April, which will always be around the time of Passover—but could be before, after, or even on Passover.