<!-- ... existing code ... -->
        function openModal(id) {
            const modal = document.getElementById(id);
            if (modal) modal.classList.remove('hidden');
        }
        function closeModal(id) {
            const modal = document.getElementById(id);
            if (modal) modal.classList.add('hidden');
        }

        function updateAuthUI() {
            const user = state.currentUser;
            const adminBanner = document.getElementById('admin-banner');
            const btnManageSuppliers = document.getElementById('btn-manage-suppliers');
            const btnFabAdd = document.getElementById('btn-fab-add');
            const authIcon = document.getElementById('auth-icon');
            const authLabel = document.getElementById('auth-label');
            const userNameEl = document.getElementById('user-display-name');
            const userRoleEl = document.getElementById('user-role-badge');

            if (user) {
                if (adminBanner) adminBanner.classList.remove('hidden');
                if (btnFabAdd) btnFabAdd.classList.remove('hidden');
                if (userNameEl) userNameEl.textContent = user.displayName || user.username;
                if (userRoleEl) userRoleEl.textContent = user.role === 'admin' ? '总店管理员' : '专线供应商';
                
                if (btnManageSuppliers) {
                    if (user.role === 'admin') {
                        btnManageSuppliers.classList.remove('hidden');
                    } else {
                        btnManageSuppliers.classList.add('hidden');
                    }
                }

                if (authIcon) authIcon.className = "fa-solid fa-user-check text-rose-500 text-sm";
                if (authLabel) authLabel.textContent = user.displayName || user.username;
            } else {
                if (adminBanner) adminBanner.classList.add('hidden');
                if (btnFabAdd) btnFabAdd.classList.add('hidden');
                if (btnManageSuppliers) btnManageSuppliers.classList.add('hidden');
                if (authIcon) authIcon.className = "fa-solid fa-user-gear text-sm";
                if (authLabel) authLabel.textContent = "管理登录";
            }
        }

        function handleAuthButtonClick() {
<!-- ... existing code ... -->
```

### Summary of Changes:
- Added guard checks for `adminBanner`, `btnFabAdd`, `btnManageSuppliers`, `userNameEl`, `userRoleEl`, `authIcon`, and `authLabel` before manipulating `.classList` or `.textContent`.
- Resolved the `TypeError: Cannot read properties of null` error during page initialization.