Firefox private browsing is designed for privacy protection
https://www.bleepingcomputer.com/news/security/firefox-now-blocks-cross-site-tracking-by-default-in-private-browsing/
Mozilla says that Firefox users will be protected against cross-site tracking automatically while browsing the Internet in Private Browsing mode.
This is because, starting with the Firefox 89 version released today, the Total Cookie Protection will be enabled by default in Private Browsing windows.