When does Brandenburg-Prussia Level 2's early Stage III card count as Stage III and when does it count as Stage II?

When does Brandenburg-Prussia Level 2's early Stage III card count as Stage III and when does it count as Stage II?

It only counts as Stage II for "What Invader Stage is the game in?" (E.g., for the Second Wave Scenario, the Ward the Shores Scenario, Events, or the rules for playing with Beasts tokens but no Events.) It's still a Stage III card for anything that cares about the Stage of a specific card (e.g., the Escalation rules for Combining Two Adversaries, or Fractured Days' unique power "The Past Returns Again").
It ceases to be special once it leaves the Invader Deck (even if it returns to the deck, e.g., via "The Past Returns Again") or gets shuffled with other Stage III cards (e.g., by the Fractured Days innate power "Visions of a Shifting Future").
This is the only specially-placed Invader card that acts differently; all other cards act like their printed Stage in all circumstances.