Remove use of drupal_static() for compatibility with FrankenPHP

Problem/Motivation

Drupal is very slowly moving to support persistent app servers as described in #2218651: [meta] Make Drupal compatible with persistent app servers like ReactPHP, PHP-PM, PHPFastCGI, FrankenPHP, Swoole. Key module's use of drupal_static() can cause keys to be exposed to the wrong user in such an environment, so we should refactor the caching to be clearly per request.

I'm opening this MR as an experiment against 1.x because that's what I'm using to test my site, but it should almost certainly be committed to Key 2.x instead.