How to change files from the deployment server to local ones using browserSync proxy?

Question

gulp.js

Hello!
There is a deploy server on which the application is running.
I need that when opening localhost:3000 browserSync replaces certain files from the server deployment with local files.
For example:
the page requests
src="/public/dist/js/database_import_edit.bundle.js",
browserSync needs to take this path and replace it with the path to the local file.
Task for browserSync

gulp.task("watch", function () {
    browserSync.init({
        proxy: "http://example.lan",
        files: ["./public/dist/js/**"],
        serveStatic: ["./public/dist/js/"],
        rewriteRules: [
            {
                match: new RegExp("dist/js/database_import_edit.bundle.js"),
                fn: function() {
                    return "browsersync/database_import_edit.bundle.js"
                }
            }
        ]
    });
    gulp.watch(webcontrol_dir + "js/**/*.js", gulp.series("build:js"));
});