Welcome to the forum!
This problem is mostly over my head (beyond my experience). But one thing I can say is that Inkscape does not have true CMYK print model support. It does have options to use cmyk color values, but cannot produce a drawing which can be printed in true CMYK.
So if Inkscape "sees" a true CMYK profile in your SVG file, it probably doesn't know how to handle it -- probably doesn't have any kind of code to preserve the CMYK in the PDF.
If the SVG file does have the true CMYK profile, then it must not have been created by Inkscape originally. Is that correct? If the image was created with Inkscape, because you misunderstood about the cmyk, then there may be a bug to be investigated in Inkscape. But I'm not sure that would help you, if your goal is to produce a true CMYK print model, using Inkscape.
For the current version of Inkscape, I don't think there is any route to the true CMYK print profile. But in older versions, there was an extension which could export an SVG image to PDF, with the true CMYK. If you used an older version of Inkscape, and we can still find a download of that extension, I'm thinking maybe it could be helpful.....somehow. But if I recall correctly, all the older versions of that extension have been removed (because its developer is working on a "new and improved" extension - all we know is that it's "under development" with no updates about when it might be available).
Well, as I said, most of your problem is outside my experience, and I can't help very much. But maybe someone else will know more about it, and can give you some helpful direction.
Edit
I might have been wrong about that old extension being withdrawn from the internet. It looks like you can download it from this page. I can't read Portuguese, but in about the middle of the page are 2 text links - 1 for an INX file and another for a PY file. Together, those make the extension. As for which version of Inkscape you'll need, I'm not sure. I would try 0.48 first. If it won't work with that one, try 0.47.
Well, you could try it with the current stable version of Inkscape (0.92.1) but I would be surprised if it works.
