Thank you very much, @rob day., very informative as always.
Yes, I was thinking about converting the whole content to the grayscale destination (images, text, line art, shapes and so forth).
But then, the resulting document will have "Black Ink - FOGRA XY" set in its Output Intent and not "FOGRA XY" as required by the printer. These things are related, but not the same (when you view these Black Ink images with the Black Ink simulation, that's not really the same as viewing them with the right CMYK simulation, am I correct?).
So I was thinking, how about changing the resulting PDF in Acrobat? I made a preflight profile for the conversion to PDF/X "FOGRA XY", but I hope that the grayscale content will not be affected or converted during the process. I hope that it will remain as it is.
I think that only the Output Intent will change, am I correct? This is important, cause additional conversions are not desirable.
I will also remove all the ICC profiles from the objects in the PDF, so that they won't cause 4-color grays.
Thanks
P.S. There's one more problem: I don't know how Indesign treats untagged grayscale content. Will it be treated as sGray or Gray Gamma 1.8 or 2.2?
I don't know how Indesign treats untagged grayscale content. Will it be treated as sGray or Gray Gamma 1.8 or 2.2?
InDesign ignores gray profiles and treats placed grayscale objects as if they are on the CMYK black plate. There are two softproof modes for grayscale images: When Overprint/Separation Preview are off, grayscales are previewed as sGray (2.1 Gamma), and when Overprint/Separation Preview are on (or there is transparency on the page with a CMYK Transparency Blend Space), the soft proof is handled by the document’s assigned CMYK profile. Neither softproof mode affects the output numbers, which you can get from Separation Preview. More here:
https://community.adobe.com/t5/indesign-discussions/greyscale-jpegs-or-psd-images-are-going-much-darker-when-dropped-in-on-indesign/m-p/11152264
Overprint Off:

With OP on the document’s assigned CMYK profile is used to preview the Black plate. The image‘s embedded Gray profile (Black Ink - ISO Coated V2) is ignored, and Black Ink - Coated FOGRA 39 is used for the softproof.

If I change the document’s assigned profile to US Sheetfed Coated, the grayscale preview is adjusted to preview as Black Ink-US Sheetfed Coated. The output values do not change:
