CiviCase: Accordions not toggle ("Roles" "Activities"). Menu Options ("Add Activity" etc.) not "auto-trigger," Admin menus at top of screen not open
All my problems stemmed from one module I installed to make adjusting the new theme easier: SwitchTheme. After installing the new theme, I installed SwitchTheme 7.x-1.x-dev on all environments. I was so caught up in theme-tweaking that when I spotted this CiviCase error, I'd forgotten about SwitchTheme. Additionally, it's such a tiny, minor module, I really hadn't expected it to have such a big impact on site behavior.

Disabling SwitchTheme 7.x-1.x-dev in Drupal's Modules page immediately resolved the issue.