I reached out to our Sales Engineering team, and here is what they suggested:
We don't have a working example of this and it is not likely a very simple concept to implement like that. More than likely some java libraries will need to be used in order to authenticate with Kerberos. Here's a project that I have found that might be useful as a starting point, but would require either wrapping this in a module or rewriting it in a way to work within jython.
Good luck, and if you get this to work, please do share with the rest of us!
I was able to get "Basic" to work without issues. The issue is how to make it work in Ignition without hardcoded credentials of any sort as this is unaccepted in any business.
If it helps, there are a few topics on the forum related to secrets management, they can help give you some ideas on how to keep hardcoded credentials out of your Ignition scripts (if you can tolerate BASIC auth):
Newer versions of PI Web API support OIDC, which might be more doable?