Replaces the old analytics_options.yaml with a new analysis_options.yaml at the workspace root, consolidating lint rules and analyzer settings. Updates all references in subprojects to use the new file, and adds flutter_lints as a direct dev dependency in pubspec.yaml for consistent linting across the workspace.
Relocated all app directories (client, design_system_viewer, staff) and their contents under the new 'apps/mobile' path. This change improves project organization and prepares for future platform-specific structuring.
