Styled App Bar - Copy this React, Mui Component to your project

Create-a-visually-appealing-and-functional-website-header-inspired-by-the-Nest-Grocery-website.-The-header-should-feature-a-prominent-logo-on-the-left-side-to-establish-brand-identity.-It-must-include-a-centrally-located-search-bar-with-intuitive-placeholder-text-like-"Search-for-groceries-or-products"-and-a-magnifying-glass-icon-for-easy-search-functionality.-The-navigation-menu-should-span-horizontally-and-include-dropdown-menus-for-major-categories-such-as-Fruits-&-Vegetables,-Dairy,-Snacks,-Beverages,-and-more.-These-dropdown-menus-should-feature-sub-menus-that-include-links-accompanied-by-visually-rich-images-and-additional-nested-links-for-enhanced-navigation.-Incorporate-user-account-options-with-icons-and-links-for-Login/Sign-Up,-as-well-as-a-user-profile-section.-Add-a-shopping-cart-icon-displaying-the-number-of-items-within,-and-a-wishlist-icon-for-easy-access-to-saved-items.-Include-dynamic-call-to-action-buttons-such-as-"Start-Shopping"-or-"Special-Deals,"-prominently-displayed-for-user-engagement.-Additionally,-provide-a-compact-top-bar-showcasing-a-promotional-banner-for-current-offers,-discounts,-or-free-delivery-announcements.-Enhance-user-convenience-with-quick-access-to-contact-and-support-links,-as-well-as-dropdown-selectors-for-location-and-language-preferences.-The-header-must-also-have-a-responsive-design-that-adapts-seamlessly-to-various-screen-sizes,-incorporating-a-collapsible-menu-for-mobile-views.-Ensure-the-aesthetic-combines-modernity-with-freshness,-leveraging-a-green-and-white-color-palette-with-minimalistic-accents.-The-dropdown-menus-should-maintain-a-sleek-appearance,-with-visually-engaging-images-and-neatly-organized-links,-elevating-both-usability-and-design-appeal.