SPOILERS!
Seldon's "public" plan was that the (First) Foundation, on Terminus, would grow into the Second Galactic Empire. Seldon's "secret" plan was that the Second Foundation would emerge as a perfect rulers guided by psychohistory. That's as far as the original books went.
Asimov revisited things, though. The "double secret backup" plan, hatched by Seldon's family/associates, involved the creation of the world-mind Gaia which would expand into the unified Galaxia mind. At the end of the the last book, chronologically, this appears to be the inevitable direction, as the thousands of years of plotting by R. Daneel Olivaw to safeguard humanity against internal and external threats comes to fruition.
However, Brin's prequel teases that a galactic hive mind would not need the written Encyclopedia Galactica entries that preface each chapter in the Foundation stories, and that perhaps things take a different turn.