Rework provider selector and settings UX

Surface all enabled providers in the model selector with inline loading
and error states instead of silently hiding non-ready ones. Tap any row
to drill in; loading and error states show in the drill-down body, with
a Retry button on error. Providers with no models render a synthetic
"Default" row so every provider's drill-down has symmetric structure.

Redesign the per-provider settings sheet: search lives in the header,
discovered and custom models share one scrolling list, and the footer
hosts action buttons. Diagnostic and "Add model" each open as their own
sub-sheet, so neither expands inline or shifts the surrounding layout.

Snapshot refresh now keeps cached data visible: setQueryData replaces
the cache atomically and sibling-scope caches are invalidated (not
removed), so refreshing a provider no longer blanks its row. Search
inputs across the app are uncontrolled — onChangeText drives parent
state, and resetKey remounts the field when an explicit reset is needed
— to avoid RN's controlled-input flicker.

Adds a dev-only mock-slow provider whose discovery never resolves, so
the 30s snapshot timeout produces a real error and lets loading and
timeout-error UI be exercised end to end.

packages/app/src/components/ui/combobox.tsx

@@ -156,7 +156,6 @@ function ComboboxSheetBackground({ style }: BottomSheetBackgroundProps) {
 
 export interface SearchInputProps {
   placeholder: string;
-  value: string;
   onChangeText: (text: string) => void;
   onSubmitEditing?: () => void;
   autoFocus?: boolean;
@@ -166,7 +165,6 @@ export interface SearchInputProps {
 
 export function SearchInput({
   placeholder,
-  value,
   onChangeText,
   onSubmitEditing,
   autoFocus = false,
@@ -194,9 +192,7 @@ export function SearchInput({
           // @ts-expect-error - outlineStyle is web-only
           style={SEARCH_INPUT_STYLE}
           placeholder={placeholder}
-          initialValue={value}
           resetKey={resetKey}
-          value={value}
           onChangeText={onChangeText}
           autoCapitalize="none"
           autoCorrect={false}
@@ -204,12 +200,12 @@ export function SearchInput({
         />
       ) : (
         <TextInput
+          key={resetKey}
           ref={inputRef}
           // @ts-expect-error - outlineStyle is web-only
           style={SEARCH_INPUT_STYLE}
           placeholder={placeholder}
           placeholderTextColor={theme.colors.foregroundMuted}
-          value={value}
           onChangeText={onChangeText}
           autoCapitalize="none"
           autoCorrect={false}
@@ -1041,7 +1037,6 @@ function MobileComboboxBody(props: MobileBodyProps): ReactElement {
           {!props.hasChildren && props.searchable ? (
             <SearchInput
               placeholder={props.searchPlaceholder}
-              value={props.searchQuery}
               onChangeText={props.setSearchQueryWithCallback}
               onSubmitEditing={props.handleSubmitSearch}
               autoFocus={false}
@@ -1150,7 +1145,6 @@ function DesktopComboboxOptionsBody(props: {
       {props.header || !props.searchable ? null : (
         <SearchInput
           placeholder={props.searchPlaceholder}
-          value={props.searchQuery}
           onChangeText={props.setSearchQueryWithCallback}
           onSubmitEditing={props.handleSubmitSearch}
           autoFocus