How do I get the URL of a right-clicked link sent to an automator action?

Try this code on Automator action "Run Javascript".

for Chrome

function run(input, parameters) {

    var app = Application("Google Chrome");
    app.includeStandardAdditions = true;

    var url = app.windows[0].activeTab.execute({
        javascript: 'window.getSelection().anchorNode.parentNode.href'
    });

    return url;
}

for Safari

function run(input, parameters) {

    var app = Application("Safari");
    app.includeStandardAdditions = true;

    var url = app.doJavaScript('window.getSelection().anchorNode.parentNode.href',{
        in: app.windows[0].currentTab
    });

    return url;
}

For example

Right click on the link and select "Copy link to clipboard" service, then you can get the URL.