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/desktop/components/pair-device-modal.tsx

@@ -1,4 +1,4 @@
-import { AdaptiveModalSheet } from "@/components/adaptive-modal-sheet";
+import { AdaptiveModalSheet, type SheetHeader } from "@/components/adaptive-modal-sheet";
 import { PairDeviceSection } from "@/desktop/components/pair-device-section";
 
 export interface PairDeviceModalProps {
@@ -8,11 +8,12 @@ export interface PairDeviceModalProps {
 }
 
 const SNAP_POINTS: string[] = ["82%", "94%"];
+const PAIR_DEVICE_HEADER: SheetHeader = { title: "Pair a device" };
 
 export function PairDeviceModal({ visible, onClose, testID }: PairDeviceModalProps) {
   return (
     <AdaptiveModalSheet
-      title="Pair a device"
+      header={PAIR_DEVICE_HEADER}
       visible={visible}
       onClose={onClose}
       snapPoints={SNAP_POINTS}