Eternatus, an alien Pokémon, radiates "Galar Particles" which contain massive amounts of exotic energy. Pokémon themselves are powered by "Infinity Energy" which is what gives them their types and powers. It is the Infinity Energy that reacts with the Galar Particles, so Humans can't do it, which powers the Pokémon. Because Pokémon can manipulate their Infinity Energy to use their powers, they then manipulate the Galar Particles as well, which for some reason are affected by a Pokémon's imagination.
I say it is imagination-based because Gigantamax forms can't be bred through genes, and often have elements that defy biology (Garbodor's toys are made of congealed gases and light)
The Pokémon's imagination influences the form they take, so some dreamers can Gigantamax but the usual masses can't.
The Galar particle-infused Infinity Energy then becomes what is essentially a psychic hardlight construct which can channel more Infinity Energy into massive attacks.

Wishing Stars are debris from the meteor that Eternatus came in, so are the Max Raid points, the strange hexagonal stones. They still carry a charge of Galar Particles.

Anon? Anon are you awake?