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/provider-selection/provider-selection.test.ts

@@ -99,14 +99,39 @@ describe("combined model selector data", () => {
     ).toEqual([]);
   });
 
-  it("excludes providers that are not ready", () => {
+  it("surfaces non-ready providers with their state-specific selection", () => {
     expect(
       buildSelectableProviderSelectorProviders([
         snapshotEntry({ provider: "loading-provider", status: "loading", models: [] }),
-        snapshotEntry({ provider: "error-provider", status: "error", models: [] }),
-        snapshotEntry({ provider: "unavailable-provider", status: "unavailable", models: [] }),
+        snapshotEntry({
+          provider: "error-provider",
+          status: "error",
+          error: "boom",
+          models: [],
+        }),
+        snapshotEntry({
+          provider: "unavailable-provider",
+          status: "unavailable",
+          models: [],
+        }),
       ]),
-    ).toEqual([]);
+    ).toEqual([
+      {
+        id: "loading-provider",
+        label: "loading-provider",
+        modelSelection: { kind: "loading" },
+      },
+      {
+        id: "error-provider",
+        label: "error-provider",
+        modelSelection: { kind: "error", message: "boom" },
+      },
+      {
+        id: "unavailable-provider",
+        label: "unavailable-provider",
+        modelSelection: { kind: "error", message: "Unavailable" },
+      },
+    ]);
   });
 
   it("builds selector providers from an already-curated provider list", () => {