Sidebar state stays put when switching post types

A round of fixes for the folder sidebar, mostly aimed at users juggling Media and Posts in the same session.

What's fixed

• Expanded folders and sidebar width are now remembered separately for each folder-enabled post type. Jumping between the Media library and Posts no longer overwrites the other's tree state.
• Folder search in the sidebar is case-insensitive — typing "invoice" matches "Invoices" without retyping.
• The sidebar now only persists UI state (expanded folders, sidebar width) instead of caching the entire folder tree, keeping browser storage lean.