The $hourIndex = (int)$hourIndex - 3; should be reverted to its initial state since the timezone is correct.

The time zone here is -3
but as I said earlier when arriving at 21:00 hours, the module stops working.

Joomla is already configured in the correct time zone.
honestly, I have no idea what is happening.

Also since you are using a 24hour schedule you have to specify the extra hours in the array. I took the liberty of adding it to the module on your site.

This will be included in the next version so you don't need to backup this edit.

Also since you have not specified any content after 21:00 the module will stop since the next entry is at 00:00.

I think I found the problem.
I used the "echo" to see the date and is 3 hour early.

Edit: The extra fields were already included in the array
As I did some testing, I ended up re-using the old code and deleted some extra fields.
Even added these extra field also on the schedule module

Apparently joomla is not saving the correct time, so I used a different code.