[SalesForce] Unable to redirect to the record created using Quick Action in lightning experience

You can try force:refreshView, which reloads all data for the view. So in addition to $A.get("e.force:closeQuickAction").fire(); add $A.get('e.force:refreshView').fire(); in your setCallback method.

({
    handleClick : function(component, event, helper) {
        var saveLeadAction = component.get("c.leadSave");
        saveLeadAction.setCallback(this, function(a) {
            if (a.getState() === "SUCCESS") {
                $A.get("e.force:closeQuickAction").fire();
                $A.get('e.force:refreshView').fire();

            }else if (res.getState() === "ERROR") {
                console.log("Errore Saving Contact ");
            } 
        }); 
        $A.enqueueAction(saveLeadAction);
    }
})

It could be many things. Below is a general troubleshooting list for a quick action (QA) that doesn't appear on record pages:

1. Does the user have access to the object the QA is creating?
2. If it's Log a Call - does the user have Access Activities permission?
3. If it's Send Email, does the user have Send Email permissions and is email deliverability turned "on" where you're testing?
4. Does the user have record type access to the record type defined in the QA?
5. If it's a VF, Aura, or LWC QA - does the user have apex access to the controller (if one is used).
6. If it's a flow QA - does the user have the Run Flows permission or Flow User checkbox on their User record? Is the Flow activated?
7. Is the page layout you added the QA defined in the page layout assignment for your profile for that record type of the record you're testing on?
8. Do you have a lightning page defined? Is it using dynamic actions? You'll have to add the QA to the dynamic actions on the lightning page itself.
9. Is the object you added the QA to a Case, Work Order, or User? This works differently in where the QA appears as noted in Actions in Lightning Experience. Depending on if feed tracking is enabled, you may see the QA in the chatter tab - utilizing dynamic actions will let you put the QA where you'd like (see this answer)

Below are more details on how to check each of the above

1. Setup --> Profiles --> UserProfile. Go to Standard Object Permissions or Custom Object Permissions to check it has create/update access.

2. Setup --> Profiles --> UserProfile. Under General User Permissions, there's the Access Activities permission that needs to be checked.

3. Setup --> Profiles --> UserProfile. Under General User Permissions, there's a Send Email permission. For Email Deliverability, go to Setup --> Deliverability and make sure Access Level is set to All Email

4. Setup --> Profiles --> UserProfile. Go to Record Type Settings, do you see the record type listed next to the object? If not, click edit and add it.

5. Setup --> Apex Classes --> YourApexClass. Click on Security and make sure the user's profile is added to the list.

6. Go to your profile and, under General User Permission, check if Run Flows is enabled. Otherwise, go to the user record itself and see if Flow User is checked.

7. Setup --> Object Manager --> YourObject --> Page Layouts. Click Page Layout Assignment and confirm the page layout you updated is assigned for the record type of the record you're on (not necessarily the one you may be creating in the QA).

8. Setup --> Object Manager --> YourObject --> Lightning Record Pages. You may need to look at View Page Assignments or what is the Org Default page, but once you figure out which page is displayed to your user, click into it and edit it. On your highlights panel, do you see an Add Action button or an Upgrade to Dynamic Actions. If you see an Add Action, you'll have to add your QA there.