Salesforce Lightning Aura Component can be used to open external url from the Global Actions. Using init handler, we can use e.force:navigateToURL to open the external URL. e.force:closeQuickAction event can be fired in afterRender to close the Quick Action Panel.

Steps:

1. Create the following Lightning Aura Component.

Sample Code:

Lightning Aura Component:

<aura:component 
                implements="force:lightningQuickActionWithoutHeader" >
    <aura:handler 
                  name="init" 
                  value="{!this}" 
                  action="{!c.onInit}"/>
</aura:component>

Lightning Aura JavaScript Controller:

( {
    
    onInit : function(
        component, event, helper
    ) {
        
        console.log( 
            'Inside onInit'
        );
        let urlEvent = $A.get(
            "e.force:navigateToURL"
        );
        urlEvent.setParams( {
            "url": 'https://www.google.com'
        } );
        urlEvent.fire(); 
        
    }
    
} )

Lightning Aura Renderer JavaScript Controller:

( {
    
    afterRender  : function( 
        component, helper
    ) {
        
        console.log( 
            'Inside afterRender Action' 
        );
        $A.get( 
            "e.force:closeQuickAction" 
        ).fire();
        
    }
    
} )

2. Create a Global Action.

3. Add the Global Action to the Publisher Layout.

Output: