What do you use for the DC to notice the beast, its passive Stealth?
I think the Automatic Success variant is meant to cover tasks that are too easy for the character to bother with making a check, whereas a passive score represents a reasonable average effort.
last first - an average effort is not the same as a minimal result - which is what passive scores tend to be used as - its how they are treated mechanically. So, "average" is not how they are used.
Both the auto-success and the passive perc establish an automatic scale for success. It would have been nice if they were tied together mechanically instead of being two different ways - treating perception alone differently.
As for the stealth passive question - its *almost* "passive stealth" - but when one shifts the die roll from one side to the other *and* keeps "ties go to roller" (IE "meet the DC or exceed equals success") then one has to use 12 not 10.
So a hiding/sneaking stealth+4 creature vs a perception +6 character would result in the PC rolling perception+6 vs 12+4 = DC 16 resulting in the same 55% being spotted and 45% remaining hidden odds as the normal 5e way to resolve it with the creature rolling stealth+4 vs the character's Dc 16 passive Perception.