EF core DbContext in a multithreaded API application

You should create a scope whenever your TimedHostedServices triggers.

Inject the service provider in your constructor:

public MyServiceService(IServiceProvider services)
{
    _services = services;
}

and then create a scope whenever the task triggers

using (var scope = _services.CreateScope())
{
    var anotherService = scope.ServiceProvider.GetRequiredService<AnotherService>();

    anotherService.Something();
}

A more complete example is available in the doc

Another approach to create own DbContextFactory and instantiate new instance for every query.

public class DbContextFactory
{
    public YourDbContext Create()
    {
        var options = new DbContextOptionsBuilder<YourDbContext>()
            .UseSqlServer(_connectionString)
            .Options;

        return new YourDbContext(options);
    }
}

Usage

public class Service
{
    private readonly DbContextFactory _dbContextFactory;

    public Service(DbContextFactory dbContextFactory) 
         => _dbContextFactory = dbContextFactory;

    public void Execute()
    {
        using (var context = _dbContextFactory.Create())
        {
            // use context
        }
    }
}    

With factory you don't need to worry about scopes anymore, and make your code free of ASP.NET Core dependencies.
You will be able to execute queries asynchronously, which not possible with scoped DbContext without workarounds.
You always be confident about what data saved when calling .SaveChanges(), where with scoped DbContext there are possibilities that some entity were changed in other class.