As alluded above, I work on a file in Indesign and then I uplaod it to photoshop to add the image (seeing that InDesign has some issues with showing greyscale images properly when needed for print) - but the issue becomes that I then have the Type compress so harshly that it often impacts the look of the work (see image below)
I know I should porobaly just be using InDesign for such jobs, but i'm not as well versed there and also have bumped into issues there regarding greyscale images.
Grayscale will reproduce correctly in InDesign if you take some precautions.
There is no grayscale color management in InDesign or indeed outside Photoshop at all. So you have to use a grayscale profile in Photoshop that matches the intended output, otherwise you get tonal shifts. If there was grayscale color management in InDesign that wouldn't be necessary, but there isn't and it is.
A grayscale file in InDesign will simply output to the K channel, the black plate. So you need to know the CMYK profile that will be used on press. You need to know that in any case, so just ask the printer if you don't know.
You can then set up Black Ink <CMYK profile> as working gray in Photoshop. Once that is done, you can pick that in Edit > Convert to Profile, and the numbers will be correctly converted and the file will be correctly reproduced in InDesign.
In the working gray rolldown, navigate to the CMYK profile used: