fix(sidebar): move search below Header, remove section chevrons

- Search input now renders between Sidebar.Header and first Section
  instead of above Header (fixes cameleer3-server#120)
- Remove ChevronRight/ChevronDown from section headers — the entire
  row is already clickable, chevrons added visual noise

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

src/design-system/layout/Sidebar/Sidebar.tsx

@@ -1,11 +1,9 @@
-import { type ReactNode } from 'react'
+import { type ReactNode, Children, isValidElement } from 'react'
 import {
   Search,
   X,
   ChevronsLeft,
   ChevronsRight,
-  ChevronRight,
-  ChevronDown,
 } from 'lucide-react'
 import styles from './Sidebar.module.css'
 import { SidebarContext, useSidebarContext } from './SidebarContext'
@@ -124,9 +122,6 @@ function SidebarSection({
         aria-label={open ? `Collapse ${label}` : `Expand ${label}`}
         onKeyDown={(e) => { if (e.key === 'Enter' || e.key === ' ') { e.preventDefault(); onToggle() } }}
       >
-        <span className={styles.treeSectionChevronBtn} aria-hidden="true">
-          {open ? <ChevronDown size={12} /> : <ChevronRight size={12} />}
-        </span>
         {icon && <span className={styles.sectionIcon}>{icon}</span>}
         <span className={styles.treeSectionLabel}>{label}</span>
       </div>
@@ -199,7 +194,20 @@ function SidebarRoot({
           </button>
         )}
 
-        {/* Search (only when expanded and handler provided) */}
+        {/* Render Header first, then search, then remaining children */}
+        {(() => {
+          const childArray = Children.toArray(children)
+          const headerIdx = childArray.findIndex(
+            (child) => isValidElement(child) && child.type === SidebarHeader,
+          )
+          const header = headerIdx >= 0 ? childArray[headerIdx] : null
+          const rest = headerIdx >= 0
+            ? [...childArray.slice(0, headerIdx), ...childArray.slice(headerIdx + 1)]
+            : childArray
+
+          return (
+            <>
+              {header}
               {onSearchChange && !collapsed && (
                 <div className={styles.searchWrap}>
                   <div className={styles.searchInner}>
@@ -226,8 +234,10 @@ function SidebarRoot({
                   </div>
                 </div>
               )}
-
+              {rest}
-        {children}
+            </>
+          )
+        })()}
       </aside>
     </SidebarContext.Provider>
   )