I can't use the Ctrl + Shift + S key combination to synchronize the colors of the images

Enhancing a frame from your video shows that the dialog box says “…metadata to file?” That is text you would find in the Save Metadata to File dialog box, not the Synchronize Settings dialog box. This suggests that there’s a problem with how the keyboard shortcut is being received, because:

The keyboard shortcut for Photo > Save Metadata to File is Ctrl+S. So it looks like Ctrl+S is the keystroke that Lightroom Classic received. But…

You are trying to press Ctrl+Shift+S for Settings > Sync Settings.

Obviously, Lightroom Classic is not receiving Ctrl+Shift+S because it ran the Save Metadata to File command (Ctrl+S) instead. 

So you should troubleshoot why Lightroom Classic is not receiving the Shift key press. Maybe there is a problem with the Shift key on that side of the keyboard? Try the Shift key on the other side. Also, try other Shift key shortcuts in Lightroom Classic, or in other applications, to try and narrow down whether the Shift key is being blocked at the application level or the OS level.

There may be a second problem, too.

The text in the dialog box says “…file” so that means one file is selected. That seems to be confirmed in the filmstrip visible in the video. But the command Settings > Sync Settings is not available when only one image is selected, so pressing Ctrl+Shift+S won’t do anything anyway. If you want to Sync Settings, select more than one image. Or, if you want to do it with just one image selected, use Settings > Copy Settings instead (Ctrl+Shift+C), then select the other images and use Settings > Paste Settings (Ctrl+Shift+V).

Your video shows a dialog box waiting to be dismissed, but it is not possible to see details of that.

Is this a Lightroom Classic warning window, or something completely other? If not Lightroom related, some other utility is probably receiving and responding to your Ctrl+Shift+S keypresses - before they can reach Lightroom Classic.

Could be a keyboard, graphics tablet or mouse driver, something of that general sort - so, running all of the time and always “first in line” for your keyboard input - within which “Ctrl+Shift+S” is set up to mean something relevant to that utility.