Does the scroll direction change for the built-in Trackpad?
If not, then try rebooting the laptop to see if it fixes it and whether changing the setting afterwards now works.
Try creating a new user account, log out of your current user account & log into the new user account. Can you configure the Bluetooth mouse properly now? If so, then maybe the mouse/trackpad .plist file in your main user account is corrupt. If so, then delete that file which would be located in the "Preferences" folder within the home user folder's hidden Library folder. You can access this hidden Library folder by clicking the Finder's "Go" menu and holding the Option key which will allow the hidden Library folder to appear on the "Go" menu. Select the hidden Library folder and navigate to the Preferences folder. Look for a file for the mouse/trackpad which begins with "com.apple.xxxxxx" where "xxxxxx" should be mouse or trackpad or something similar.
Try booting the laptop into Safe Mode to see whether it helps in which case it may indicate a problem with some third party software you have installed.
Did you install any Logitech software to use with your mouse? If so, then you may need to use that software to configure the mouse, or it may have its own "Logitech" icon within the System Preferences.