perf(backend): cache YouTube searches and shrink the thumbnail URLs

Repeated searches and song lookups now reuse a single-flight memory cache, so
concurrent or debounced queries hit YouTube once instead of on every keystroke.
Thumbnails are resolved at a configurable size instead of the largest variant,
which cuts the image payload the browser pulls from Google.

backend/Musify.Infrastructure/Services/SingleFlightCache.cs

@@ -0,0 +1,41 @@
+using System.Collections.Concurrent;
+using ErrorOr;
+using Microsoft.Extensions.Caching.Memory;
+
+namespace Musify.Infrastructure.Services
+{
+    public sealed class SingleFlightCache(IMemoryCache cache)
+    {
+        private readonly ConcurrentDictionary<string, object> inFlight = new();
+
+        public async Task<ErrorOr<TValue>> GetOrCreateAsync<TValue>(
+            string key,
+            TimeSpan duration,
+            Func<Task<ErrorOr<TValue>>> factory)
+        {
+            if (duration <= TimeSpan.Zero)
+                return await factory();
+
+            if (cache.TryGetValue(key, out TValue? cached) && cached is not null)
+                return cached;
+
+            var pending = (Lazy<Task<ErrorOr<TValue>>>)inFlight.GetOrAdd(
+                key,
+                _ => new Lazy<Task<ErrorOr<TValue>>>(factory));
+
+            try
+            {
+                var result = await pending.Value;
+
+                if (!result.IsError)
+                    cache.Set(key, result.Value, duration);
+
+                return result;
+            }
+            finally
+            {
+                inFlight.TryRemove(key, out _);
+            }
+        }
+    }
+}