It is not possible to embed permissions in the files. Even if I wanted to do that, it isn’t possible.
I have access to a Plesk server so I uploaded the latest zip and extracted it.
I see there has been a change with the default permissions that Plesk uses. The permissions on files are correct, but the permissions on directories are missing the Write setting that osTicket needs.
If you select the main directory > Change Permissions > check Owner / Write and check Change permissions recursively it should work for you.
Thanks for letting me know about this. I will include this note for Plesk when I update the Installation Instructions.