在BackgroundService中使用IServiceScopeFactory和IServiceScope来创建新的作用域，并在该作用域中进行数据库操作，以便BackgroundService可以看到数据库更新。

代码示例：

在Startup.cs中配置服务并将DbContext注册为Scoped服务：

public void ConfigureServices(IServiceCollection services)
{
    // other configurations
    services.AddDbContext(options =>
        options.UseSqlServer(Configuration.GetConnectionString("MyConnectionString")));

    services.AddScoped();
}

在BackgroundService中注入IServiceScopeFactory并使用它来创建新的作用域：

public class MyBackgroundService : BackgroundService
{
    private readonly ILogger _logger;
    private readonly IServiceScopeFactory _serviceScopeFactory;

    public MyBackgroundService(ILogger logger, IServiceScopeFactory serviceScopeFactory)
    {
        _logger = logger;
        _serviceScopeFactory = serviceScopeFactory;
    }

    protected override async Task ExecuteAsync(CancellationToken stoppingToken)
    {
        while (!stoppingToken.IsCancellationRequested)
        {
            using (var scope = _serviceScopeFactory.CreateScope())
            {
                var myService = scope.ServiceProvider.GetService();
                await myService.DoSomethingAsync(stoppingToken);
            }

            await Task.Delay(5000, stoppingToken);
        }
    }
}

在IMyService的实现类（MyService）中使用依赖注入的DbContext进行数据库操作：

public class MyService : IMyService
{
    private readonly MyDbContext _dbContext;

    public MyService(MyDbContext dbContext)
    {
        _dbContext = dbContext;
    }

    public async Task DoSomethingAsync(CancellationToken stoppingToken)
    {
        // do some database operations here
        await _dbContext.MyEntities.AddAsync(new MyEntity());
        await _dbContext.SaveChangesAsync(stoppingToken);
    }
}