Poisoning as an attack in Pokemon TCG
The Super Intense Poison attack of Toxapex-GX says:


   Super Intense Poison
  Your opponent's Active Pokémon is now Poisoned. Put 10 damage counters instead of 1 on that Pokémon between turns.


Special Conditions (including Poisoned) are considered an effect of an attack. It is not related to damage in any way. The second sentence alters the number of damage counters that are put on your opponent's Active Pokémon between turns, but this is also not considered damage.

Bent Spoon is a Pokémon Tool with this effect:


  Bent Spoon - Item - Pokémon Tool
  Prevent all effects of your opponent's attacks, except damage, done to the Pokémon this card is attached to. (Existing effects are not removed.)


Because the effect of Super Intense Poison is just creating an effect (Poison) on the targeted Pokémon, Bent Spoon prevents this effect from happening.

As a result, if your opponent's Active Pokémon has Bent Spoon attached, your Toxapex-GX's Super Intense Poison attack does nothing.

The "Put 10 damage counters instead of 1 on that Pokémon between turns." part is also prevented, so if your opponent's Active Pokémon is already Poisoned, the Poison does not get changed into 10-damage one.