You don't just need Generations to allude to it. Sonic Adventure 1 is built directly upon plot threads from Sonic 1, 2, 3 & Knuckles, and CD. Not just upon plot threads, but upon revisiting the same settings and expanding upon them, to the degree that Ice Cap is in both games. The whole story is based around confirming that the island from Sonic 3 & Knuckles was originally part of the same island that Station Square is on, which also further implies that Station Square is on Westside Island, the island from Sonic 2.
To say later games are a different continuity or a different world wouldn't just separate them from the 2D games, it would separate them from Sonic Adventure, which would just be ridiculous.
Though Sonic Mania technically is a different timeline, since it follows from "Classic Sonic's" alt-timeline created when the Time Eater invaded Green Hill Zone near the beginning of Sonic 1's time in Generations. Ironically, "Classic Sonic" is specifically not the Sonic from the "Classic" era games, Modern Sonic is. This is why Modern Sonic remembers being in the old locations, but not meeting his own future self. This shouldn't be hard to understand, but people are dumb and don't pay attention.