does this variant exist?
I never saw a CV like this. Your Tank reminds me of mine in Invasion (http://history.chess.free.fr/invasion.htm) although is different. Your Wizard is similar to the Paratrooper of my Invasion too. Your Soldier is not clear for me, is it a Pawn which also can capture straight forward? Your Long Knight seems the one generally called a Camel.

One more thing... If you sign up, the notation will be like normal chess. No letter for soldier, we use algebraic notation. L for long knight, K for king, W for wizard, A for archer, T for tank.
For example, a first move for white could be e3. Then black might do Lc5. Then Ad3 for white. Then d6 as black, then Axh7. (Note x is used for shooting in the case of Archers or Tanks.) Normal rules apply with check, checkmate and stalemate. If you still have a wizard on the board and you cannot block or move out of check, you may have to teleport the wizard in front.

Whoops i forgot something in the notation, three soldiers can move to e3. The e-soldier moves to e3 in this case, so it should be (e)e3

I never saw a CV like this. Your Tank reminds me of mine in Invasion (http://history.chess.free.fr/invasion.htm) although is different. Your Wizard is similar to the Paratrooper of my Invasion too. Your Soldier is not clear for me, is it a Pawn which also can capture straight forward? Your Long Knight seems the one generally called a Camel.
That’s awesome!
Soldier: Takes the place of the pawn. Moves and captures one square forward or like a pawn.
Long knight: Takes the place of the knight. Moves or captures three squares forward and one to the side and can jump over pieces.
Archer: Takes the place of the Bishop. Moves one square forward, to the side, or backwards or one or two diagonally. Captures by shooting arrows three or more squares diagonally. (Shooting means it captures that piece, but does not occupy the captured piece’s square)
Tank: Takes the place of the rook. Moves one square diagonally or two to the side, forward or backwards. Captures by shooting three or more squares diagonally.
Wizard: Takes the place of the queen. Moves by teleporting to any unoccupied square on the board. Only captures like a queen.
King: If you’re on chess.com you probably know what a king is.