After switching from PHP 5 to 7 for a local 2.x install, I can't login
Turns out that it was a PHP configuration issue.

Under Windows, the paths in php.ini need to include a drive letter (eg. c:\xampp\php7\). By default they're root-relative (eg. \xampp\php7). When I originally installed XAMPP with PHP 5.x, it adjusted the paths automatically. But when I manually copied the PHP 7 folder into XAMPP to set it up for version switching, I overlooked the path discrepancy.

In this case, it was the inability of PHP 7 to set sessions that was causing the odd behavior.