After exiting private browsing, Firefox does not delete cookies.
After exiting private browsing, Firefox does not delete cookies. For example, the site: https://4pda.to leaves cookies from the site: devapps.ru | And if the site that I visit is built to redirect to another site, then the cookies of the first site remain in the browser. Try to go with Russian IP to https://aliexpress.com/ and you will be redirected to https://aliexpress.ru/ while the cookies from the first site (aliexpress.com) remain. Manual blocking in Firefox does not work in this case (devapps.ru), adding in block with Adguard helps. The screenshot shows the last two cookies that appeared in normal mode after using private browsing. And my settings. Chrome doesn't have this problem.
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What you see in "Settings -> Privacy & Security
Cookies and Site Data: Manage Data" are cookies from a regular session and not PB mode cookies.
Firefox has two two cookie jars, one for regular windows stored in cookies.sqlite in the profile folder and one for all Private Browsing windows kept in memory. Cookies in the PB jar that is kept in memory (i.e. not stored in the profile folder) are shared among all PB Windows and PB Tabs and are purged automatically if you close all PB mode windows or close Firefox.
If you run Firefox in permanent Private Browsing mode (Always use Private Browsing mode; Never Remember History) then you can't remove the regular mode cookies shown in Manage Data, to remove those you need to exit permanent Private Browsing mode.
I wrote that after working in private mode, I close it to the dick, after which I open a regular browser and there are cookies from private mode. Open the site https://4pda.to/ in private mode, after closing the private mode, open a regular browser and tell me if you will have devapps.ru cookies