There are a few problems here:
- on Windows you often have the problem that the OPENSSL_CONF Windows environment setting is not correct. With previous Prestashop versions that was no problem but now it is. OPENSSL_CONF points to an openssl.cnf file. Xampp is supposed to set that but it doesn't. Older Prestashop versions didn't check for that. If you have a standard Xampp installation its value should be C:\xampp\apache\bin\openssl.cnf. After that you need to restart.
- there is another problem that the module ps_edition_basic requires PHP 8.1. This module comes only with the commercial version of Prestashop. When you download from Github (https://github.com/PrestaShop/PrestaShop/releases/tag/8.1.1) this module is not included. As Github is used for upgrades this problem doesn't play with upgrades. An alternative is to delete this module under the /modules directory. After the first run of the installation and before you click to retry the files are present and you can access them.