This is at best only a partial match, but I'll mention it in case you've misremembered the story or conflated it with another story. Anyhow, my suggestion is Hallucination by Isaac Asimov. I read it in his anthology Gold.
A young scientist called Sam Chase is sent to a planet (simply called Energy Planet in the story) to investigate hallucinations being experienced by staff on the planet. He finds insect like creatures that are hexagonal as you describe:
One of them landed on his finger and Sam looked at it curiously. It was very small and, therefore, hard to see in detail, but it seemed hexagonal, bulging above and concave below. There were many short, small legs so that when it moved it almost seemed to do so on tiny wheels. There were no signs of wings till it suddenly took off, and then four tiny, feathery objects unfurled.
Sam discovers the insects link together as you describe to form a hive mind:
“Not an individual insect by itself, but they fit together when they want to, like little jigsaw pieces. They can do it in any way they want. And when they do, their nervous systems fit together, too, and build up. A lot of them together are intelligent."
But the planet is not sending out pulses of energy. It's called energy planet because it is in orbit around a neutron star and humans wish to use it to generate energy. This would destroy the insects' hive mind hence the insects are generating the hallucinations in an attempt to communicate with humans.
The stort also does not end with a quote of the type you describe and there is no suggestion that the planet is part of any galactic mind.