It’s not floating at sea level, but it doesn’t even extend to sea level. The base of the mountain is well above sea level. If you live in a flat part of New Mexico, South Africa, or Mongolia you’re significantly higher above sea level than someone in England, Eastern Europe, or Mississippi. If you think of the mountain as extending below sea level you start seeing (tectonic) mountain ranges as like Aspen forests, where it’s just a single thing. Such as the Rocky mountain and the Himalaya mountain, while volcanic mountains such as the Cascades and Hawaii remain ranges.

But yeah differentiating where a new mountain starts vs just another peak of the same one isn’t necessarily easy