大家好，提前感谢您提供的支持。
我找到了解决问题的方法。
基本上我已经将所有调用AccessToken方法的方法转换为异步方法，这意味着，从Web方法（控制器）到内部方法，它们现在都是异步的。下面是所有相互调用的方法，直到调用AccessToken方法：

public class SharePointController : ApiController
{
    [AllowAnonymous]
    [HttpGet]
    [Route("api/sharepoint/connect")]
    public async Task<bool> Connect()
    {
        var obj = new SPConnection())
        
        return await obj.ConnectWithToken();
        
    }
}
    
    
    public class SPConnection
        {
    public async Task<bool> ConnectWithToken()
        {
            var authority = $"https://login.microsoftonline.com/{this.AzureTenantId}/";
            var token = await GetAccessToken(this.AzureCertFile, this.AzureCertPassword, this.AzureClientId, this.AzureTenantId, this.AzureTenantName, authority);
    
            using (var context = new ClientContext(this.SiteUrl))
            {
                context.ExecutingWebRequest += (s, e) =>
                {
                    e.WebRequestExecutor.RequestHeaders["Authorization"] =
                        "Bearer " + token;
                };
    
                this.Web = context.Web;
                context.Load(Web,
                               w => w.Title,
                               w => w.Url,
                               w => w.Lists);
                await context.ExecuteQueryAsync();
    
                this.ClientCtx = context;
            }
    
            return true;
        }
    
        private async Task<string> GetAccessToken(string azureCertFile, string azureCertPassword, string azureClientId, string azureTenantId, string azureTenantName, string authority)
        {
            /*REQUIRED CODE HERE TO DO THIS WORKS*/
    
            try
            {
                authResult = await azureApp.AcquireTokenForClient(spScopes).ExecuteAsync();
            }
            catch (MsalUiRequiredException ex)
            {
                // The application doesn't have sufficient permissions.
                // - Did you declare enough app permissions during app creation?
                // - Did the tenant admin grant permissions to the application?
            }
            catch (MsalServiceException ex) when (ex.Message.Contains("AADSTS70011"))
            {
                // Invalid scope. The scope has to be in the form "https://resourceurl/.default"
                // Mitigation: Change the scope to be as expected.
            }
            catch (Exception ex)
            {
                //Other type of exceptions
            }
    
            return authResult != null ? authResult.AccessToken : null;
        }
        }