Designing an Accepted/202 endpoint

Question

I have an end point where a user can start an update operation. I don't want to make the user wait for the result. There are two possible outcomes:

1. The action is succesful - nothing to do for the user.
2. There is an exception - this is logged (every exception is) in WatchDog and the database admin checks this.

[HttpPatch("{joborderID}/[Action]")]
[SwaggerResponse(202)]
public IActionResult UpdateBlozoColumns(int joborderID)
{
    joborderService.UpdateBlozoColumnsIfNecessary(joborderID);
    return Accepted();
}

The UpdateBlozoColumnsIfNecessary:

internal async Task UpdateBlozoColumnsIfNecessary(int joborderID)
{
    // Do something
}

Visual Studio warns:

Because this call is not awaited, execution of the current method continues before the call is completed. Consider applying the 'await' operator to the result of the call.

Now if I am correct, when there is an exception, it isn't catched because it is in a task? How can I write this that the accepted-pattern is correct?

Would a "fire and forget" pattern be appropiate?

Task.Run(async () =>
{
    try
    {
        await joborderService.UpdateBlozoColumnsIfNecessary(joborderID);
    }
    catch (Exception ex)
    {
        throw;
    }
});

return Accepted();

Or

var task = joborderService.UpdateBlozoColumnsIfNecessary(joborderID);

task.ContinueWith(task =>
{
    if (task.Exception is not null)
    {
        throw task.Exception;
    }
});