InDesign - batch update stylesheets across multiple files?

Make a copy of the folder with the files and try this JS:

var myFolder = Folder.selectDialog("Select the folder containing InDesign Files", "");
var f = myFolder.getFiles("*"+ ".indd");
var ps;
// note that appliedFont is the font and style separated by a tab
var nf = "Arial\tBook";

for (var i = 0; i < f.length; i++){
    //set the 2nd parameter set to false hides the files when they are opened
    var doc = app.open(File(f[i]), true);
    
    try{
		ps = doc.paragraphStyles.item("Foo Style");
        ps.appliedFont = nf;
        doc.close(SaveOptions.YES)
	} catch (e){}
};   

You might want to check out this link https://redokun.com/blog/indesign-scripts that contains a long list of both free and paid InDesign scripts to see if a script exists to do what you're looking for.

You could all all of the files to an InDesign Book file, then use Syncronize to push the changes across all book documents. 

If you do this, be sure to first uncheck all options except for Paragraph Styles (and Character Styles, if applicable)

This will only work if there are not other same-name styles with differnet definitions.  

The other way would be to import only the Foo style into each document, but I don't think you can batch that. (unless it would be possilbe with a script, but that is outside of my expertise)