What most people visually recognise as the SCOBY isn’t actually the yeast or bacteria (even though they live within it) but a mat of cellulose – the same stuff that makes up the fibre in plants. SCOBYs will start off as thin translucent films and if the microbes in your kombucha are healthy and thriving the SCOBY will thicken as it ferments (most often into a smooth surfaced, opaque sheet, that is tan to white in appearance). Its buoyancy means it usually floats, but it may move around, sink, bubble up, or even tilt on its side as the mixture ferments and that’s totally fine.
The older a SCOBY gets, the wispier and browner it may become. However, even if the SCOBY never grows large or thick, it doesn’t mean your kombucha has failed! Some liquids are just better at providing the raw building blocks the microbes need to construct a thick mat, but in its absence, it doesn’t mean they aren’t fermenting.