Let say that I have a rectangular object with some mixed content (visually like acoustic spectrum for example). How to fold/wrap it into a circular form?

Hi.

Polar coordinates are available on raster editors, like gimp.
If all are vectors, there would some problems appear -like how to distort a gradient fill--->using gradient meshes...

In general, I'd say it is not possible yet, BUT
if it's just distorting an "acoustic spectrum" then you can use a simple pattern along path lpe where the pattern would be the spectrum and the core path a circle.

I'm not entirely sure what an acoustic spectrum is. But from what I imagine it is, it seems like it might be possible to clip the rectangle with a circle or ellipse. It would not change the contents of the rectangle, but would give it a round border. Can you show an example what it is?

It's not clear to me if the OP is wanting a 2D circle or 3D cylinder.

Was thinking of a circular equalizer from the original post, like the one in this video.

Briefly, from something like this into something like this or this.

So in rectangular form, the view will be vectorized for further editing, and then it has to be folded to form a circle.

Oh gosh no! You'd need some kind of dedicated sound software to convert that. Or maybe some kind of software that can create different kinds of graphs....so you would enter the data, and then have it spit out this kind of graph and that kind of graph. I assume there's some kind of software that can do that, but I don't really know.

There's an Inkscape extension called Nice Charts (https://github.com/Florianjw/NiceCharts) which I guess creates charts. I haven't used it, so I can't share any experience. I guess I'd be surprised if it can do that, but Inkscape is full of surprises! (Although if it can do that, I'd be even more surprised if it could do it in color.)

Could find three relevant topic:

polar transform in inkscape

drawing a polar chart

polar coordinates

The last link has an example file to be used with blender, where you can add a video for the texture to be distorted then and can render animations with it after but I doubt that would be the case.
For a still image, a pattern along path lpe can fulfill the need.