docs: fix stale results in Icons search (#9802)

Author: reidbarber

packages/dev/s2-docs/src/MobileSearchMenu.tsx

@@ -315,13 +315,13 @@ function MobileNav({initialTag}: {initialTag?: string}) {
               <MobileTabPanel key={library.id} id={library.id}>
                 <Autocomplete
                   key={isTypographySelected ? 'typography' : 'default'}
+                  inputValue={searchValue}
+                  onInputChange={handleSearchChange}
                   filter={showIcons ? iconFilter : undefined}
                   disableVirtualFocus={isTypographySelected}>
                   <div className={stickySearchContainer}>
                     <SearchField
                       aria-label="Search"
-                      value={searchValue}
-                      onChange={handleSearchChange}
                       onFocus={handleSearchFocus}
                       onBlur={handleSearchBlur}
                       placeholder={placeholderText}
@@ -403,4 +403,3 @@ function MobileNav({initialTag}: {initialTag?: string}) {
     </div>
   );
 }
-

packages/dev/s2-docs/src/SearchMenu.tsx

@@ -163,13 +163,13 @@ export function SearchMenu(props: SearchMenuProps) {
             <TabPanel key={tab.id} id={tab.id}>
               <Autocomplete
                 key={selectedTagId === 'typography' ? 'typography' : 'default'}
+                inputValue={searchValue}
+                onInputChange={setSearchValue}
                 filter={isIconsSelected ? iconFilter : undefined}
                 disableVirtualFocus={selectedTagId === 'typography'}>
                 <div className={style({display: 'flex', flexDirection: 'column', height: 'full'})}>
                   <div className={style({flexShrink: 0, marginStart: 16, marginEnd: 64})}>
                     <SearchField
-                      value={searchValue}
-                      onChange={setSearchValue}
                       ref={searchRef}
                       size="L"
                       aria-label={`Search ${tab.label}`}