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/components/combined-model-selector.test.ts

@@ -3,6 +3,7 @@ import type { AgentModelDefinition } from "@server/server/agent/agent-sdk-types"
 import {
   buildModelRows,
   buildSelectedTriggerLabel,
+  filterAndRankModelRows,
   matchesSearch,
   resolveProviderLabel,
 } from "./combined-model-selector.utils";
@@ -83,6 +84,34 @@ describe("combined model selector helpers", () => {
     expect(matchesSearch(row, "kimi gemini")).toBe(false);
   });
 
+  it("ranks model search results by fuzzy match quality", () => {
+    const rows = [
+      {
+        favoriteKey: "openai:gpt-4.1",
+        provider: "openai",
+        providerLabel: "OpenAI",
+        modelId: "gpt-4.1",
+        modelLabel: "GPT-4.1",
+      },
+      {
+        favoriteKey: "openai:gpt-5.4",
+        provider: "openai",
+        providerLabel: "OpenAI",
+        modelId: "gpt-5.4",
+        modelLabel: "GPT-5.4",
+      },
+      {
+        favoriteKey: "google:gemini",
+        provider: "google",
+        providerLabel: "Google",
+        modelId: "gemini",
+        modelLabel: "Gemini",
+      },
+    ];
+
+    expect(filterAndRankModelRows(rows, "gpt54").map((row) => row.modelId)).toEqual(["gpt-5.4"]);
+  });
+
   it("keeps the selected trigger label model-only", () => {
     expect(resolveProviderLabel(providerDefinitions, "codex")).toBe("Codex");
     expect(buildSelectedTriggerLabel("GPT-5.4")).toBe("GPT-5.4");