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").
If you would Accelerate it out of the deck, instead discard the next Stage II card underneath it (or the top-most Stage III card if there are no Stage II cards left).
Visions of a Shifting Future can't bury it to the bottom of the deck (since it's specially placed during Setup), but can shuffle it to take a chance at delaying it.
If you instead choose to put the top Invader Card on the bottom of the deck, resolve the reminder card before moving on with the rest of the Slow Power Phase.