Hey, @paulabender!
That’s unusual. But rest assured we are committed to finding out what is going on!
Let’s try to start fresh here so we can make sure we did not miss anything.
I see your staging site https://carlabjoyas.com.ar/test/ is already on the storefront theme, right?
It already has only WooCommerce active, right? If it does not, please deactivate everything but Woo again.
Please remove all shipping methods including CABA. Then add the free shipping to CABA again, from scratch. You can also add one other method (like pick up) so we can compare.
Please share screenshots of how the new shipping is set up step by step, both free shipping and pick up.
Do you have any custom code on the site? If you do, please let us know and remove it.
Then, please share the SSR to the staging site again so we can also take a look at how it is now.
Looking forward to your reply.
Have a wonderful day!