In January 1996, a TV commercial aired in Japan (in a time slot reserved by Sony) announced that Final Fantasy VII would be a PS1 game. For Sega, who learned this at the same time as everyone else, it meant its negotiations with Square to release the game on Saturn had failed.
1995 was a good year for Sega in Japan sales wise, and in the weeks preceding this announcement, 3 of the 10 best selling Saturn games in Japan were released: Virtua Fighter 2, which for a long time remained Sega's only million seller in that country, Sega Rally and Virtua Cop.
This announcement had a direct impact on Sega's console sales in Japan, even though 1996 was still a good year for the Saturn in that market. Moreover, Sega of Japan still had hopes that the Saturn would win the battle against the PS1.
For Hisashi Suzuki, former head of Sega's R&D department, Final Fantasy VII also marks a symbolic turning point for the arcade market, which has definitively lost its battle against the consumer market with the release of this game.
This announcement came at a time when several Super Famicom games developed by Square (including Super Mario RPG and Bahamut Lagoon) had not yet been released and most people expected Square to continue its collaboration with Nintendo.
It probably helped that Square's 3DCG demo shown at the SIGGRAPH '95 was often mislabeled as an N64 demo - it was developed on a Silicon Graphics station called ONYX, at a time when Nintendo and Silicon Graphics were collaborating on the N64.
Sources:
https://news.denfaminicogamer.jp/kikakuthetower/191015a/2
https://www.4gamer.net/games/999/G999905/20190302005/