Add ErrorHandlingMiddleware for consistent JSON error responses

Catches all unhandled exceptions, logs them, and returns
{ "error": "An unexpected error occurred." } with HTTP 500.
Registered before all other middleware so nothing leaks through.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/Budget.Api/Program.cs

@@ -126,6 +126,7 @@ using (var scope = app.Services.CreateScope())
 }
 
 app.UseForwardedHeaders();
+app.UseMiddleware<ErrorHandlingMiddleware>();
 
 app.UseDefaultFiles();
 app.UseStaticFiles();

src/Budget.Api/Services/ErrorHandlingMiddleware.cs

@@ -0,0 +1,21 @@
+using System.Text.Json;
+
+namespace Budget.Api.Services;
+
+public class ErrorHandlingMiddleware(RequestDelegate next, ILogger<ErrorHandlingMiddleware> logger)
+{
+    public async Task InvokeAsync(HttpContext context)
+    {
+        try
+        {
+            await next(context);
+        }
+        catch (Exception ex)
+        {
+            logger.LogError(ex, "Unhandled exception");
+            context.Response.StatusCode = StatusCodes.Status500InternalServerError;
+            context.Response.ContentType = "application/json";
+            await context.Response.WriteAsync(JsonSerializer.Serialize(new { error = "An unexpected error occurred." }));
+        }
+    }
+}