Since Booster Energy is restored after battle when consumed (as are all non-Berry items as of Pokémon Scarlet and Violet), it can be obtained from wild Paradox Pokémon even if it was consumed during battle.
Booster Energy was introduced as Pokémon Tool cards in the Pokémon Trading Card Game during the English Scarlet & Violet Series (the Japanese Scarlet & Violet Era) as Ancient Booster Energy Capsule and Future Booster Energy Capsule. They were first released in Japanese in the Ancient Roar and Future Flash expansions, respectively, before being released in the English Paradox Rift expansion. Both cards support the Paradox Pokémon they are attached to: Ancient Booster Energy Capsule provides the Ancient Pokémon it is attached to with an additional 60 HP and immunity to all Special Conditions, while a Future Pokémon with a Future Booster Energy Capsule attached has no Retreat Cost and its attacks do 20 more damage to the opponent's Active Pokémon.