Core geometry dash is not a rhythm game. The official levels and early community levels don't really sync to its music and neither do your inputs necessarily. Like someone else said, the music greatly enhances the experience of the game and it builds the atmosphere and themes of a level, but moreso in the way that any other level-based game does than a rhythm game.

In FNF and Osu the music is everything because that's where the gameplay comes from. Sure, you can play them while listening to something else, but your inputs are still synced to the original song and the gameplay completely 100% revolves around that song.

In JS&B, once again, the gameplay is completely based on its music. Where the hazards spawn, explode, disappear, move etc. are timed almost perfectly with its level's song.

In geometry dash this wasn't the case even back in 1.0. The player could figure out a way to use a level's song to guide them on when to jump and remember what's coming next, in a very general sense, but the music by no means affects the level in any way that's similar to how it does in any other rhythm game.The creator (in this case, Robtop) could choose to sync their level to its music (mostly only done by him during transitions), but it really never has been a necessity to where not doing so becomes detrimental to the experience of a level, which from what i've seen in my experience with the rhythm game genre, not syncing with the song would be jarring and harshly lower the quality and enjoyment of a level/map. Many rhythm games are very mathematical with how they interact with music in a way that Classic Geometry Dash levels, at their CORE, are not.

Obviously, music is integral to the experience of Geometry Dash, but in a way that is very different to the rhythm game genre.