Honestly, the Caves & Cliffs update hasn't been that great so far. Like, sure, the new generation is awesome, but not enough to carry the whole update. I think the second wave is going to bring better stuff.
You’re probably in your old server. To find new generation, I’m pretty sure you need to go far away from your original spawn.
If its a new server, Some terrains does not spawn such as the lush caves or the geodes; it requires a single biome setting.
But the new mobs are cool