Thanks guys. I added in PHP.ini the following date.timezone = Europe/Athens and also I cleaned installed Zencart 2.0 tested with PHP 8.11 and PHP 8.3. The problem is the same. When I go to PHP 8.0 the installation works. The logs of ZC 2.0 are listed below. No patch was added in ZenCart 2.0.

[10-May-2024 11:04:23 Europe/Athens] PHP Fatal error: Uncaught IntlException: datefmt_create: No such time zone: 'Europe/Athens': U_ILLEGAL_ARGUMENT_ERROR in /includes/classes/zcDate.php:89
Stack trace:
#0 /includes/classes/zcDate.php(89): IntlDateFormatter->__construct()
#1 /includes/classes/zcDate.php(39): zcDate->initializeConversionArrays()
#2 /includes/autoload_func.php(47): zcDate->__construct()
#3 /includes/application_top.php(253): require('...')
#4 /index.php(25): require('...')
#5 {main}
thrown in /includes/classes/zcDate.php on line 89