Response caching and output caching do not cache headers modified in OnStarting handler

### Is there an existing issue for this?

- [X] I have searched the existing issues

### Describe the bug

Response caching does not cache headers modified in the OnStarting delegate in middleware loaded after responsecaching middleware.

``` c#
context.Response.OnStarting(CheckIfHeaderNeeded, context);

private Task CheckIfHeaderNeeded(object state)
{
var context = (HttpContext)state;
context.Response.Headers.Remove("removeme");
return Task.CompletedTask;
}
```

revmoveme header will only be removed on the initial request

### Expected Behavior

Response caching should cache the actual final headers sent to the client. It cannot cache only headers created before the await(next) in middleware.

This will also fix #23218 if I understand the issue correctly.

@Tratcher mentioned one possible fix is
> One fix would be for the caching middleware to shim OnStarting and run those callbacks before it captured the headers. (Complex)

That seems to be the correct behavior

### Steps To Reproduce

https://github.com/lawrencek76/header-caching-issue

### Exceptions (if any)

_No response_

### .NET Version

6.0.101

### Anything else?

Initially ran into this trying to cache security headers with a nonce in another middleware.
https://github.com/andrewlock/NetEscapades.AspNetCore.SecurityHeaders/issues/117

After attempting to make a pr to fix this in the other middleware I realized there is really no way I can find to really do this correctly outside of the caching middleware itself.

https://github.com/andrewlock/NetEscapades.AspNetCore.SecurityHeaders/pull/118