I need to call an external API that requires to send its key as a query string. The API has GET and POST endpoints. In both endpoints, there are no (currently) other parameters in queries

So, an example query should look like
https://example.com/service?key={key value}

I want to not add the query at all places where I call the client and rather configure it on the startup.

Normally, the examples I see put query strings as part of the route to the HTTP client with the question mark in between the route and query.

Is it possible to inject a key as a query string on startup without writing complicated extensions/logic?

I set up the injection like

    var settings = configuration.GetSection(nameof(ApiSettings)).Get<ApiSettings>();

    services.AddHttpClient<IMyService, MyService>
        (client =>
        {
            client.BaseAddress = new Uri(settings.BaseAddress);
        });

and then consume it like

 public class MyService : IMyService
    {
        private readonly IHttpClientFactory _httpClientFactory;

        public MyService(IHttpClientFactory httpClientFactory)
        {
            _httpClientFactory = httpClientFactory;
        }

        private HttpClient CreateClient() => _httpClientFactory.CreateClient();
        
        public async Task<RouteDetails> GetRouteDetails(ICollection<Point> points)
        {
            var httpClient = CreateClient();
            var response = await httpClient.PostAsync($"/api/poi", new JsonContent(points));
...
        }
    }

I am looking for something easy to read and not too much extra code. I believe plenty APIs consume their access keys as a query string, so, there should be an out-of-the-box solution that I am missing.

I can also reference Refit if it is easier.