Improve mobile selectors and sheet inputs

Keep sheet text inputs native-owned to avoid React Native controlled input flicker during fast typing. Add reset keys for fields that need programmatic clears, and move model, mode, and thinking pickers onto shared combobox rows with fuzzy ranked search and native virtualization.

packages/app/src/screens/settings/host-page.tsx

@@ -18,7 +18,7 @@ import { confirmDialog } from "@/utils/confirm-dialog";
 import { settingsStyles } from "@/styles/settings";
 import { Button } from "@/components/ui/button";
 import { Switch } from "@/components/ui/switch";
-import { AdaptiveModalSheet } from "@/components/adaptive-modal-sheet";
+import { AdaptiveModalSheet, type SheetHeader } from "@/components/adaptive-modal-sheet";
 import { useDaemonConfig } from "@/hooks/use-daemon-config";
 import { useIsLocalDaemon } from "@/hooks/use-is-local-daemon";
 import { SettingsSection } from "@/screens/settings/settings-section";
@@ -68,6 +68,10 @@ function formatDaemonVersionBadge(version: string | null): string | null {
   return trimmed.startsWith("v") ? trimmed : `v${trimmed}`;
 }
 
+const RENAME_HOST_HEADER: SheetHeader = { title: "Rename host" };
+const REMOVE_CONNECTION_HEADER: SheetHeader = { title: "Remove connection" };
+const REMOVE_HOST_HEADER: SheetHeader = { title: "Remove host" };
+
 export interface HostPageProps {
   serverId: string;
   onHostRemoved?: () => void;
@@ -244,7 +248,7 @@ export function HostRenameButton({ host }: { host: HostProfile }) {
       <AdaptiveModalSheet
         visible={isEditing}
         onClose={handleCancel}
-        title="Rename host"
+        header={RENAME_HOST_HEADER}
         testID="host-page-rename-modal"
       >
         <View style={styles.renameBody}>
@@ -347,7 +351,7 @@ function ConnectionsSection({ host }: { host: HostProfile }) {
 
       {pendingRemoveConnection ? (
         <AdaptiveModalSheet
-          title="Remove connection"
+          header={REMOVE_CONNECTION_HEADER}
           visible
           onClose={handleCloseConfirm}
           testID="remove-connection-confirm-modal"
@@ -723,7 +727,7 @@ function RemoveHostSection({ host, onRemoved }: { host: HostProfile; onRemoved?:
 
       {isConfirming ? (
         <AdaptiveModalSheet
-          title="Remove host"
+          header={REMOVE_HOST_HEADER}
           visible
           onClose={handleCloseConfirm}
           testID="remove-host-confirm-modal"