Printing module does not work properly

By "Print Module" am I right to presume that you mean the Print dialog created by Photoshop? I think so.

This issue seems like it might be the macOS Big Sur printer profile issue, updating should fix that.

There is apparently a bug in macOS Big Sur 11.6.2 in connection with ICC profile use/printing 

- users are reporting that the update to macOS 11.6.5 fixes the print issues.

Otherwise, perhaps you'd like to work through the following: 

ON a MAC, reset printing system:

On your Mac, choose Apple menu System Preferences, then click Printers & Scanners

Press and hold the Control key as you click in the list at the left, then choose “Reset printing system” from the menu that appears.

After you reset the printing system, the list of printers in Printers & Scanners preferences is empty.

Reinstall the print driver, only from the manufacturer, not Apple.

Also take a look at the following article and check if that helps: 

https://helpx.adobe.com/photoshop/using/printing-color-management-photoshop1.html

You may like to re-install the printer drivers to check if that makes a difference?

Here is some general Adobe [Mac and Win] info on printing problems,

https://helpx.adobe.com/photoshop/kb/troubleshoot-printing-problems.html

Simple reset: hold the space bar when you open the print window. It resets the print dialogs

if that doesn’t help -

Perhaps try resetting Photoshop preferences?

(read this entire post before acting please)

Resetting restores Photoshop's internal preferences, which are saved when Photoshop closes.

If they become corrupt then various issues can occur.

Here’s some info on how to do that:

Manually removing preferences files is the most complete method for restoring Photoshop to its default state: 

https://helpx.adobe.com/photoshop/using/preferences.html#Manually

The user Library folder is hidden by default on macOS.

To access files in the hidden user Library folder, see here for how to access hidden user library files. https://helpx.adobe.com/x-productkb/global/access-hidden-user-library-files.html

Unexpected behavior may indicate damaged preferences. Restoring preferences to their default settings is a good idea when trying to troubleshoot unexpected behaviors in Photoshop. check out the video

https://helpx.adobe.com/photoshop/using/preferences.html#reset_preferences

Learn how to access and modify Photoshop preferences and customize per your frequent workflows

https://helpx.adobe.com/photoshop/using/preferences.html

And here’s an earlier forum discussion as an aid to understanding

https://community.adobe.com/t5/photoshop-ecosystem-discussions/quick-tips-how-to-reset-photoshop-preferences/td-p/12502668

You may want to backup your settings and custom presets, brushes & actions before restoring Photoshop's preferences.

Here is general info about that:  https://helpx.adobe.com/photoshop/using/preferences.html#BackupPhotoshoppreferences

Preferences file locations: https://helpx.adobe.com/photoshop/kb/preference-file-names-locations-photoshop.html

Note that on macOS:

1:The user Library folder is hidden by default on macOS. To access the hidden user Library folder, see this How To:

https://helpx.adobe.com/x-productkb/global/access-hidden-user-library-files.html

2: preference preservation is affected by macOS permissions,

you’ll need to allow Photoshop ‘Full Disk Access’ in your Mac OS Preferences/Security and Privacy

I hope this helps
neil barstow, colourmanagement net :: adobe forum volunteer:: co-author: 'getting colour right'
google me "neil barstow colourmanagement" for lots of free articles on colour management