Adds initNavGroupState() and saveNavGroupState() functions so the
open/closed state of each .mode-nav-dropdown survives page reloads.
Active groups are never force-closed even if localStorage says closed.
Adds test_nav_state.py with two tests verifying presence of the
functions and data-group attributes on all five nav groups.
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
