There is no continuity where warp travel became obsolete. Discovery season 3 explored this a bit...
In the late 31st century there was an event called The Burn, where all dilithium went inert. Since dilithium controls warp reactions, any ship with an active warp core at the time exploded, destroying most interstellar travel. What we see is that, while there were attempts at replacing warp, the Federation in particular fell apart because there was no way to travel between systems at impulse. While scientists worked to build a replacement, we see no working replacements when Discovery comes upon what remains of Starfleet nearly 100 years later. In other words, none of the "alternative warp" tech we see throughout the Trek universe seems to pan out.
Discovery, which is the only ship with a working spore drive (and a full stock of dilithium) winds up as the only ship that can traverse large distances easily. Starfleet still has other ships than can travel at warp, but as they lack steady supplies of dilithium, those ships are sparsely used.
By the end of Season 4, it's become known that the Federation is heavily invested in making the Spore Drive work on a larger scale (the Emerald Chain was also investing in the technology), since it's superior to warp in many respects, given that it can move a ship anywhere in the Milky Way galaxy. We already see some of those fruits borne out by Book's ship also having a working spore drive (Book is natively able to act as a conduit for the drive in both his ship and Discovery).