perf: add pagination to game selection view

Fixes lag and color inconsistency in trip creation game selection.
- Add pagination with 50 games per page to TripCreationViewModel
- Add displayedAvailableGames, loadInitialAvailableGames, loadMoreAvailableGames
- Update GamePickerSheet to use paginated data with infinite scroll trigger
- Show "Load more games" button with progress indicator and count

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

SportsTime/Features/Trip/ViewModels/TripCreationViewModel.swift

@@ -112,6 +112,28 @@ final class TripCreationViewModel {
     var availableGames: [RichGame] = []
     var isLoadingGames: Bool = false
 
+    // MARK: - Game Pagination
+    private let gamePageSize = 50
+    var displayedAvailableGames: [RichGame] = []
+    private var currentGamePage = 0
+
+    var hasMoreAvailableGames: Bool {
+        displayedAvailableGames.count < availableGames.count
+    }
+
+    func loadInitialAvailableGames() {
+        currentGamePage = 0
+        displayedAvailableGames = Array(availableGames.prefix(gamePageSize))
+    }
+
+    func loadMoreAvailableGames() {
+        guard hasMoreAvailableGames else { return }
+        currentGamePage += 1
+        let start = currentGamePage * gamePageSize
+        let end = min(start + gamePageSize, availableGames.count)
+        displayedAvailableGames.append(contentsOf: availableGames[start..<end])
+    }
+
     // Travel
     var travelMode: TravelMode = .drive
     var routePreference: RoutePreference = .balanced
@@ -276,6 +298,9 @@ final class TripCreationViewModel {
                 }
                 return RichGame(game: game, homeTeam: homeTeam, awayTeam: awayTeam, stadium: stadium)
             }
+
+            // Initialize paginated display
+            loadInitialAvailableGames()
         } catch {
             viewState = .error("Failed to load schedule data: \(error.localizedDescription)")
         }
@@ -501,6 +526,9 @@ final class TripCreationViewModel {
                 return RichGame(game: game, homeTeam: homeTeam, awayTeam: awayTeam, stadium: stadium)
             }.sorted { $0.game.dateTime < $1.game.dateTime }
 
+            // Initialize paginated display
+            loadInitialAvailableGames()
+
         } catch {
             viewState = .error("Failed to load games: \(error.localizedDescription)")
         }
@@ -541,6 +569,8 @@ final class TripCreationViewModel {
         mustStopLocations = []
         preferredCities = []
         availableGames = []
+        displayedAvailableGames = []
+        currentGamePage = 0
         isLoadingGames = false
         currentPreferences = nil
         allowRepeatCities = true