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/provider-settings-host.tsx

@@ -0,0 +1,26 @@
+import { useCallback } from "react";
+import { ProviderDiagnosticSheet } from "@/components/provider-diagnostic-sheet";
+import { useProviderSettingsStore } from "@/stores/provider-settings-store";
+
+export function ProviderSettingsHost() {
+  const serverId = useProviderSettingsStore((state) => state.serverId);
+  const provider = useProviderSettingsStore((state) => state.provider);
+  const close = useProviderSettingsStore((state) => state.close);
+
+  const handleClose = useCallback(() => {
+    close();
+  }, [close]);
+
+  if (!serverId || !provider) {
+    return null;
+  }
+
+  return (
+    <ProviderDiagnosticSheet
+      provider={provider}
+      serverId={serverId}
+      visible
+      onClose={handleClose}
+    />
+  );
+}