Some central aspects (a race that modified itself to become floating spheres) match a race in "All Tomorrows", by C.M. Kosemen, an SF work (not a novel, but a future history told through an illustrated catalogue of bizarre future races) which does not mention the traveling protagonist you described, but among the descendent races of humans described by the work are the "Gravitals", a daughter species that forsook the humanoid form of their "Ruin Haunter" forebears in favor of the form of floating spheres.
The Ruin Haunters, who were lucky enough to inherit the secrets of the Star Men
and Qu when other species were mere animals, had experienced a tremendous advance
in technological prowess. All in all they were as sophisticated as, if not more, than the Asteromorphs of the void. But their ascendancy was not a sane one. Recall that most Ruin Haunters were already deranged with a twisted assumption of being the sole inheritors of the Star Men. They refused to communicate with their relatives on other planets, and kept to their own affairs. This neurotic hubris assumed truly dangerous proportions after the Ruin Haunters modified themselves.
The origin of this modification lay in an earlier catastrophe. The Ruin Haunters’ sun was undergoing a rapid phase of expansion, and the species, advanced as it was, could do nothing to stop the process. So the Haunters did the next best thing, and changed their bodies.
The infernal conditions of the solar expansion meant that a biological
reconstruction was totally out of the question. Thus, the Haunters replaced their bodies with machines; floating spheres of metal that moved and molded their environment through subtle manipulations of gravity fields. In earlier versions the spheres still cradled the organic brains of the last Haunters. But in successive generations, ways of containing the mind within quantum computers were devised, and the transformation became absolute. The Ruin Haunters were replaced by the completely mechanical Gravital.
I normally might avoid giving (or at least hesitate to suggest) an identification answer with such major mismatches (the presence/absence of a protagonist, the increments along the way in their transformation), but in a case like this, where the questioner asked about a work known only from a recollection of a retelling from another person's recollection, it's quite conceivable to me that significant errors crept in.