How to plot map layer in shiny using leaflet?

What you describe is a nice, if not exactly entry level, modeling and visualization exercise.

You will find the basics of shiny integration described on RStudio's Leaflet pages.

For an example of a (very simple) map app built in Shiny using the well known & much loved North Carolina shapefile that comes with {sf} consider this example; it is turned inside out compared to your use case (the map is for clicking and text is for displaying information) but it is a start...

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