My best guess would be that there is an error in the php.ini file that the install is generating.
I installed PHP 7 into an older version of XAMPP a few weeks ago and updated the php.ini myself to get it to work (I don’t have any problems with sessions). The following are the lines in my php.ini in the [Session] section that are not commented by having a ; at the start of the line.
If you compare those values with what you have in your php.ini then that may help you to work out which value is being set incorrectly to cause the problem.