Uh.
When you used Lutris to install WoW, which directory did you used as the destination?
Check the permissions of the wow install directory, did you run perhaps Lutris as root and as such the directory is only writeable from root?
You can claim ownership of that directory, but would afaik require the terminal.
But you did read, right? Linux allows you to kill itself without batting an eye…
How did you start Lutris? Did it asked you for your password?
What are the actual permissions of your wow directory? Who is the owner?
What is the Data Partition you’ve mentioned and how does it differ from other partitions Bazzit created? (What is this OS install?)
Also can you just run battle.net from Lutris and thus run wow?
Uuuh wait… Did you actually install Bazzite onto your system or are you in the live session?