I’m trying to update a third-party theme to its latest version but I don’t have the option to “Add latest theme version” in the theme store. How can I enable this button?
What do you mean by “third party theme”?
If the theme was not purchased through the shopify theme store themes.shopify.com , then the admins theme system cannot update the theme.
For off platform third party themes you must go through whatever site you used to buy the third party theme and get a new version and manually upload the theme to the theme admin.