log persistence mode in iRule

There doesn't appear to be a way to directly query a persistence type via iRule commands.

You might be able to leverage 'persist lookup' using if..else logic to check each persistence type returning true for a match.

#pseudo code
when HTTP_REQUEST {
    if { persist lookup cookie == $cookievalue }{
        log local0. "Persistence type Cookie"
    }
    else { persist lookup simple == $simplevalue }{
        log local0. "Persistence type Simple"
    }
}

https://clouddocs.f5.com/api/irules/persist.html