fix(login): show the Quick Connect code in an auto-dismissing sheet

The code was shown in a native Alert, which has no programmatic
dismiss: after another device authorized the code and polling logged
the user in, the alert stayed open on top of the app.

Replace it with an in-app bottom sheet that closes itself once the
session is authorized. Dismissing only hides the code - polling
continues so login still completes if the code is authorized
afterwards; polling stops when leaving the login screen (parity with
TVLogin). The code can be tapped to copy (expo-clipboard, probed via
requireOptionalNativeModule so builds without the native module just
no-op).

bun.lock

@@ -31,6 +31,7 @@
         "expo-brightness": "~56.0.5",
         "expo-build-properties": "~56.0.15",
         "expo-camera": "~56.0.7",
+        "expo-clipboard": "~56.0.4",
         "expo-constants": "~56.0.16",
         "expo-crypto": "~56.0.4",
         "expo-dev-client": "~56.0.16",
@@ -955,6 +956,8 @@
 
     "expo-camera": ["expo-camera@56.0.7", "", { "dependencies": { "barcode-detector": "^3.0.0" }, "peerDependencies": { "expo": "*", "react": "*", "react-native": "*", "react-native-web": "*" }, "optionalPeers": ["react-native-web"] }, "sha512-c8z+UheidFintQyP9XLEDP43aK4PS/o9+TFLW0zEOjdqkYCBgoWq6Mw/Ps62kjBeftFY7xrp5ZLITbenNvbTaw=="],
 
+    "expo-clipboard": ["expo-clipboard@56.0.4", "", { "peerDependencies": { "expo": "*", "react": "*", "react-native": "*" } }, "sha512-qb4DYlkiowHYHaUYVT2FN9nk/nI1xShXOUYsI7J9dVpQCOHcGFjCBPX1VAvEW4Ye4/Aagd6IuhOVAq/+scBOiA=="],
+
     "expo-constants": ["expo-constants@56.0.16", "", { "dependencies": { "@expo/env": "~2.3.0" }, "peerDependencies": { "expo": "*", "react-native": "*" } }, "sha512-6tsiN+gmTUPp/atyA+uY9Tg8VOdXdmb4s/3TVGolfn6A/oCAraw1pcPZX5XllyD+xUguxB6eBSFAT8494hZVMA=="],
 
     "expo-crypto": ["expo-crypto@56.0.4", "", { "peerDependencies": { "expo": "*" } }, "sha512-fRNEhoXRXgAWBpe3/hq5X+KXTit3OZqdiAGts1YvNEUHQb+H5591mpPac0Yw+sZg9pXcrjRnzo5AxvZaENpc7g=="],