When you purchase the payment plugin, you will receive a zip file called os_osm_paypalstc.zip. Go to Membership Pro -> Payment Plugins to install it as any other payment plugin. See https://docs.joomdonation.com/membershippro/basic-setup/payment-plugins#install-new-payment-plugin for installation instructions if needed.
If you are using Joomla 4.0+, it has a plugin called System - HTTP Headers . By default, that plugin will prevent the popup window to allow users to pay using their PayPal account. To prevent that issue, you will need to edit the plugin, change the Cross-Origin-Opener-Policy parameter to same-origin-allow-popups and it will work well