This story is most likely "Sporting with the Chid" (1979), by Barrington J. Bayley, which matches your description closely. Having heard that, in human religions, souls can leave bodies, the Chid (the alien race which performs the medical procedure) modify the astronaut's brain to exist independently outside of his body, and it walks around on its own.

The surrounding trees leaned over it protectively, spreading their branches to form a complete canopy above it: a little lake of blood...Dozens of small creatures were gathered on the shores of the pool to drink: segmented creatures the size of lobsters, creatures like the brain-animal they had seen already, creatures that consisted of clusters of tubes, resembling assemblies of veins and arteries.

This story is most likely "Sporting with the Chid" (1979), by Barrington J. Bayley, which matches your description closely. Having heard that, in human religions, souls can leave bodies, the Chid (the alien race which performs the medical procedure) modify the astronaut's brain to exist independently outside of his body, and it walks around on its own.

The surrounding trees leaned over it protectively, spreading their branches to form a complete canopy above it: a little lake of blood...Dozens of small creatures were gathered on the shores of the pool to drink: segmented creatures the size of lobsters, creatures like the brain-animal they had seen already, creatures that consisted of clusters of tubes, resembling assemblies of veins and arteries.

This story is most likely "Sporting with the Chid" (1979), by Barrington J. Bayley, which matches your description closely. "Chid" is the name of the alien race which performs the medical procedure.

The surrounding trees leaned over it protectively, spreading their branches to form a complete canopy above it: a little lake of blood...Dozens of small creatures were gathered on the shores of the pool to drink: segmented creatures the size of lobsters, creatures like the brain-animal they had seen already, creatures that consisted of clusters of tubes, resembling assemblies of veins and arteries.

This story is most likely "Sporting with the Chid" (1979), by Barrington J. Bayley, which matches your description closely. Having heard that, in human religions, souls can leave bodies, the Chid (the alien race which performs the medical procedure) modify the astronaut's brain to exist independently outside of his body, and it walks around on its own.

The surrounding trees leaned over it protectively, spreading their branches to form a complete canopy above it: a little lake of blood...Dozens of small creatures were gathered on the shores of the pool to drink: segmented creatures the size of lobsters, creatures like the brain-animal they had seen already, creatures that consisted of clusters of tubes, resembling assemblies of veins and arteries.