So I've been having an issue recently where Zorin OS would ask for authentication for stupid reasons that would usually be resolved automatically I will add more screenshots as I get them.
Reboot attempt from terminal (usually doesn't require admin)
Your screenshots show you as entering reboot in terminal from your User Account in Home Directory rather than in root.
To reboot, you are directing systemctl and therefor, need Root Privileges.
sudo reboot
I do not know if you did that in terminal only for the reason of providing an image of the Authentication Popup window...
Or if that is the cause of your trouble.
It is not so easy, since permissions can be changed on a case by case basis.
These are saved by the specs of the file, not in some central list of permissions that you can check.
For me, I would backup personal data and reinstall Zorin OS.
But for those that would prefer to avoid that, they may look at:
I have never used that script, so I cannot vouch for it.
I think I'll take the first option as I've also been having troubles with installing WINE, I will make a script to reinstall most (if not all) of my apps then I'll transfer all important data onto my phone, I will need to reinstall Zorin another time as I do not have access to my live USB at the moment
You could also try to create a new user account, and use that for a while to see if you get prompted for password randomly. If not, then that narrows the problem down.
In Settings -> Users -> Add User. Note that you need to unlock the "Add User" option first by entering your password. Make sure you make this user an administrator, which simply means that it has access to sudo, unless you don't need that.
I have no idea what the problem you're having is or if this would solve it, btw, I just think it may be a quick workaround. Better to re-install when you have all of your data backed up properly, to be safe, as it's quite an odd issue.
Ok Zorin has been successfully reinstalled along with the installation of wine 8.17 and the reinstallation of all the other apps that I had as well as all important data