i don't believe they will ever make a Sonic Adventure 3, its just a pipe dream by fans.
SEGA wanted to experiment outside the Adventure brand since some people complained it doesn't resemble the classic games.
But some projects since then have been influenced by these games, Shadow the Hedgehog is a continuation of the storyline, Sonic 2006 is essentially Adventure 3(just badly made) with a realistic artsyle,Sonic Unleashed started as Adventure 3 before evolving into something else, and Sonic Frontiers is the new formula that evolved from Sonic Adventure