Multiple implementation of HttpClient

Scenario:

I need to load work items from two project management systems (VSTS and Jira) through their REST API. Each of them has different authorization mechanism:

• VSTS: Using access token that load from database, varied by team/group of users
• Jira: Using personal token that load from user claims, varied by user

Basic classes and an interface:

public interface IProjectManagementClient
{
    ProjectManagementType Type { get; }
    Task<WorkItem> GetWorkItemAsync(ProjectManagement projectManagement, int id, CancellationToken token = default(CancellationToken));
    Task<List<WorkItem>> GetAllWorkItemsAsync(ProjectManagement projectManagement, string term, int limit = 10, CancellationToken token = default(CancellationToken));
}

public enum ProjectManagementType
{
    VSTS,
    Jira
}

public class ProjectManagement
{
    public int Id { get; set; }
    public ProjectManagementType Type { get; set; }
    public string BaseAddress { get; set; }
    public string AccessToken { get; set; }
}

Setup:

services.AddHttpClient<IProjectManagementClient, VstsClient>();
services.AddHttpClient<IProjectManagementClient, JiraClient>()
    .AddHttpMessageHandler(provider => new BasicAuthHandler(provider.GetService<IHttpContextAccessor>(), CustomClaimTypes.TrackerToken));

Usage example:

public TimesheetsController(IEnumerable<IProjectManagementClient> projectManagementClients)
{
    _projectManagementClients = projectManagementClients;
}

public void DoWork()
{
    foreach (var timesheet in _timesheets)
    {
        var projectManagementClient = _projectManagementClients.First(o => o.Type == timesheet.ProjectManagement.Type);
        timesheet.WorkItem = timesheet.WorkItemId.HasValue
            ? await projectManagementClient.GetWorkItemAsync(timesheet.ProjectManagement, timesheet.WorkItemId.Value, token)
            : null;
    }
}

Issues:

Even though I've only registered the BasicAuthHandler to the JiraClient. It has been applied to both VSTS and Jira clients.

Thus it has overridden the VSTS authorization that has been set previously in VstsClient.

Both works fine if I only setup and use only of them at a time. Please help.