But after redirection to account/account, session seems wiped.

You can play  with controllers to exclude extensions effect at all.
Just open controller pages/account/account and comment two rows with hooks call
i mean lines with
//$this->extensions->UpdateData();
and
//$this->extensions->InitData();

After that no one extension hooks will run. And you will be sure problem in the server configuration or in php-code.

Just add two slashes // before call.

I had previously posted regarding the persistent login loop issue in AbanteCart v1.4.1 on my live store. I received some suggestions (thanks to the contributors!) and have now tried several of those recommendations, but unfortunately, the problem still persists.

What I've Tried So Far:
Checked Session Creation
Session is successfully created after login (verified in debug logs and $_SESSION array).
customer_id, zone_id, etc. are set correctly.

Secure Cookie Handling
Set a secure, HTTP-only customer cookie using setcookie() inside ControllerPagesAccountLogin.
Cookie is visible in browser, path and domain are correct.

Session Loss After Redirection
On next request after login, session appears to be reset  user is redirected back to login.
We checked .htaccess, index.php, and ensured no session reset is triggered in code.

But after redirection to account/account, session seems wiped.

Can anyone explain to me how to change the name of SALE ?

Please check this file https://github.com/abantecart/abantecart-src/blob/master/public_html/extensions/novator/storefront/view/novator/template/blocks/product_cell_grid.tpl#L31

I am being told that my permissions are set to 755 and I keep getting errors. Cannot even update the version of abantecarte as I get these errors:

755 means write for file/directory owner and listing(reading) for group and other users.
Your web-server works under some user. Usually it's a username that your account registered. In your case it's a "heartpetsupply".
Looks like somebody uploaded your files with wrong permissions or did it by security reason.
So, you should to set 755 permissions for all directories and files in the list.
You can do this via cPanel FileManager. Just select directory, for example default_usps. Change permissions and files inside.
If you do not plan to use extensions default_usps and default_spanish(language pack), you can just delete them.

For those integrating AbanteCart into existing systems, using the internal API models is a game-changer—it streamlines syncing products, orders, and customers with CRMs or ERPs. Also, embedding the storefront via HTML is great for seamless integration with other sites. Highly recommend exploring the API docs and marketplace extensions for smoother workflows.