The Outlook object model doesn't provide any ready-made properties for that. Sensitivity labels are stored in custom properties that can be accessed by using the PropertyAccessor object. For example, to read the property you can use the following code:
var mipLabels = currentMailItem.PropertyAccessor.GetProperty("http://schemas.microsoft.com/mapi/string/{00020386-0000-0000-C000-000000000046}/msip_labels/0x0000001F") as string;
To set a property you can use the following code:
public void SetMIP_LabelPublic(MailItem newMailItem)
{
var lblID = "00012345-0000-0000-C000-0000000000XX"; // your label ID
var tenantId = "00012345-0000-0000-C000-0000000XXXXX"; // your azure information tenant (your company) id
var mipMethod = "Privileged";
var dd = DateTime.Now.ToString("yyyy-MM-ddTHH:mm:ssZ", CultureInfo.CreateSpecificCulture("en-us"));
var mipPropertyText = $"MSIP_Label_{lblID}_Enabled=true; "
+ $"MSIP_Label_{lblID}_SetDate={dd}; "
+ $"MSIP_Label_{lblID}_Method={mipMethod}; "
+ $"MSIP_Label_{lblID}_SiteId={tenantId}; ";
newMailItem.PropertyAccessor.SetProperty("http://schemas.microsoft.com/mapi/string/{00020386-0000-0000-C000-000000000046}/msip_labels/0x0000001F", mipPropertyText);
}
You can try using MFCMAPI or OutlookSpy for exploring internals of Outlook and custom property values.