I created two webhooks, but how do I conditionally send either one? Or at least disambiguate and update that is going to be called by private note added?

Under the Ticket Updates section

I added one webhook to catch general updates which is good

and then I added another webhook to only trigger when a private note is added which works as well

The issue is that when the only change in the ticket made is a private not is added it sends the update ticket as well, but I want to exclude the general update webhook when the private note webhook is added.  How do I do this?  I tried looking in the event and properties, but I can’t find a combination that will allow this.  Am I missing something?