If a Spirit's Presence counts as Beasts (say, due to Settle Into Hunting-Grounds), and a "destroy Beasts" effect destroys their Presence, is it still considered destroyed Presence? More generally, if Piece A also counts as Piece B, and a "destroy/remove Piece B" effect destroys/removes it, does it go to the supply for A or B?

If a Spirit's Presence counts as Beasts (say, due to Settle Into Hunting-Grounds), and a "destroy Beasts" effect destroys their Presence, is it still considered destroyed Presence? More generally, if Piece A also counts as Piece B, and a "destroy/remove Piece B" effect destroys/removes it, does it go to the supply for A or B?

It's considered destroyed Presence. When a piece is removed from the board, it goes to the supply (or other destination) for that physical type of piece.