fix(profiles): label a Plex Home parent connection as an account

A Plex Home profile's chip rendered the parent connection's displayLabel,
which for a Plex account is the account owner's username. The owner's name
appeared directly beneath the Home user's own, reading as the wrong user
being signed in.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Fdzda9t7kQtq7LoQ2v5nVF

lib/i18n/en.i18n.json

@@ -763,6 +763,7 @@
     "deleteThisProfileTitle": "Delete this profile?",
     "deleteThisProfileMessage": "Remove ${displayName}. Connections aren't affected.",
     "active": "Active",
+    "viaPlexAccount": "via ${name}",
     "manage": "Manage",
     "delete": "Delete",
     "signOut": "Sign out",

lib/i18n/strings.g.dart

@@ -4,7 +4,7 @@
 /// To regenerate, run: `dart run slang`
 ///
 /// Locales: 22
-/// Strings: 32946 (1497 per locale)
+/// Strings: 32947 (1497 per locale)
 
 // coverage:ignore-file
 // ignore_for_file: type=lint, unused_import

lib/i18n/strings_en.g.dart

@@ -2296,6 +2296,9 @@ class Translations$profiles$en {
 	/// en: 'Active'
 	String get active => 'Active';
 
+	/// en: 'via ${name}'
+	String viaPlexAccount({required Object name}) => 'via ${name}';
+
 	/// en: 'Manage'
 	String get manage => 'Manage';
 
@@ -6751,6 +6754,7 @@ extension on Translations {
 			'profiles.deleteThisProfileTitle' => 'Delete this profile?',
 			'profiles.deleteThisProfileMessage' => ({required Object displayName}) => 'Remove ${displayName}. Connections aren\'t affected.',
 			'profiles.active' => 'Active',
+			'profiles.viaPlexAccount' => ({required Object name}) => 'via ${name}',
 			'profiles.manage' => 'Manage',
 			'profiles.delete' => 'Delete',
 			'profiles.signOut' => 'Sign out',
@@ -7059,9 +7063,9 @@ extension on Translations {
 			'explore.stats.onHold' => ({required Object n}) => '${n} on hold',
 			'explore.stats.dropped' => ({required Object n}) => '${n} dropped',
 			'explore.season.winter' => 'Winter',
-			'explore.season.spring' => 'Spring',
 			_ => null,
 		} ?? switch (path) {
+			'explore.season.spring' => 'Spring',
 			'explore.season.summer' => 'Summer',
 			'explore.season.fall' => 'Fall',
 			'explore.season.withYear' => ({required Object season, required Object year}) => '${season} ${year}',
@@ -7573,9 +7577,9 @@ extension on Translations {
 			'externalPlayer.playerPackage' => 'Package Name',
 			'externalPlayer.playerUrlScheme' => 'URL Scheme',
 			'externalPlayer.off' => 'Off',
-			'externalPlayer.launchFailed' => 'Failed to open external player',
 			_ => null,
 		} ?? switch (path) {
+			'externalPlayer.launchFailed' => 'Failed to open external player',
 			'externalPlayer.appNotInstalled' => ({required Object name}) => '${name} is not installed',
 			'externalPlayer.playInExternalPlayer' => 'Play in External Player',
 			'metadataEdit.editMetadata' => 'Edit...',

lib/screens/profile/profile_switch_screen.dart

@@ -4,6 +4,7 @@ import 'package:flutter/material.dart';
 import 'package:material_symbols_icons/symbols.dart';
 import 'package:provider/provider.dart';
 
+import '../../connection/connection.dart';
 import '../../connection/connection_registry.dart';
 import '../../focus/focusable_wrapper.dart';
 import '../../i18n/strings.g.dart';
@@ -320,7 +321,16 @@ class _ProfileSwitchScreenState extends State<ProfileSwitchScreen> with MountedS
       final parentId = profile.parentConnectionId;
       if (parentId != null) {
         final conn = view.connectionsById[parentId];
-        if (conn != null) chips.add(_ChipData(backend: conn.backend, label: conn.displayLabel));
+        if (conn != null) {
+          chips.add(
+            _ChipData(
+              backend: conn.backend,
+              label: conn is PlexAccountConnection
+                  ? t.profiles.viaPlexAccount(name: conn.accountLabel)
+                  : conn.displayLabel,
+            ),
+          );
+        }
       }
     }
     final pcs = visibleProfileConnections(