How to convert RGB images to CMYK in a PDF exported from I

Good evening contrariness,

I am joining the conversation regarding this thorny subject. I am indeed in the process of creating a catalog of shoes... black and gray ones! The problem is that I cannot get in direct contact with the printer, which is often the case, even when explaining to the client why we want to do so.
- For the output PDF, is the setting (convert to destination/coated FOGRA39/do not include profiles) the safest option?
- I have simulated CMYK on my photos in Photoshop but did not change their profile upon importing into InDesign because there are too many and I have little time. By the way, is it useful to do this if the PDF takes care of it? And when opening the PDF, can you see this color change as it's not obvious?
Reading the above, I feel a bit lost.
Thank you in advance for your clarifications.

InDesign is only for layout. It is in Photoshop that you can assess the color of your images. For this, you have an option in the menu "View/Proof Setup"

If your screen is calibrated, you should have a good approximation of the result, an approximation because it is always possible to adjust the colors by saturating one relative to another, but this affects the overall printed form (or a strip in the direction of printing).

So if you have converted your RGB images with the desired profile to CMYK, they should print as you see them on the screen in Photoshop with the proof setup simulation. And create your PDF normally in CMYK without adding a profile unless the service provider advises otherwise.

Printing a PDF is a bit more complicated because we are no longer dealing with color separation, but with composite printing. Printers use 6 or 8 ink colors to expand the color gamut (and try to reproduce Pantone, but there is still a long way to go!!)... For proofs from a PDF, the RIP (or printer driver) must be configured (with a printing profile this time) according to the type of paper, and a calibrated proof paper.. but it costs so much that no one uses it.. or very few, like for packaging.

Always so quick, thank you. Indeed, I just checked, I did check CMYK in my proof format. But then why when I test my RGB photo in CMYK mode in Photoshop do the shoes become very dark? What should I rely on to adjust their brightness?

The RGB color space is much larger than that of CMYK, which is why the color darkens during conversion. This conversion is influenced by the CMYK profile you used in the "Edit/Color" menu (workspace).
If you have calibrated your monitor, you should find the calibration profile in the RGB display settings.

You need to play with the levels to compensate for the conversion. It's quite an art..! In the case of a catalog, it may be necessary to open several images at the same time to harmonize all those on the same page.