It doesn't copy whether that creature is tapped or untapped, whether it has any counters on it or Auras and/or Equipment attached to it, or any non-copy effects that changed its power, toughness, types, color, and so on
"Episode 4: Justice Before Mercy" Natalie : Once a member of the Azorius Senate, Alquist Proft easily hacks through their wards of the prison and gives Etrata the opportunity to escape
Number 6 Language English Legal Formats Brawl, Commander, Competitive Brawl, Historic, Legacy, Modern, Timeless, Vintage Not Legal Formats Alchemy, Pauper, Pioneer, Standard Rulings (1/24/2025) The creature that entered and caused the ability to trigger will also get a +1/+1 counter, provided it's still on the battlefield when the ability resolves.
Not all build around cards are created equal, though, and Lasting Tarfire from Lorwyn Eclipsed is a real dumpster fire of a card
Stone of Erech does passive graveyard pruning for one mana