Swagger in ASP.NET with OWIN and adding headers to response in middleware

Question

I have an ASP.NET Web API (on .NET 4.8.1) using OWIN. I have Swagger configured and it work great until I add some middleware that add some header values to all outgoing responses.

    public override async Task Invoke(IOwinContext context)
    {
        var request = context.Request;
        var appKey = "someId"; // update with correct app key
        var correlationId = GetCorrelationId(request);

        await _next.Invoke(context).ConfigureAwait(false);
        context.Response.Headers["x-api-key"] = appKey;
        context.Response.Headers["X-Correlation-ID"] = correlationId;
    }

Testing with Postman the endpoints work just fine but swagger just look like this:

swagger
  http:/example.com/api
  api_key
Explore

So for some reason adding headers to the response messes up swagger.

I run a test on a .NET 7 app and as long as I added the middleware after adding swagger it works just fine.

// Configure the HTTP request pipeline.
if (app.Environment.IsDevelopment())
{
    app.UseSwagger();
    app.UseSwaggerUI();
}

app.UseMiddleware<TestMiddleware>();

What's causing this issue and how do I solve it?