WordPress does not distinguish between server and client installations. WordPress runs wherever it is installed.
If you want to make changes to the project, there are several ways to do so. If it’s just a matter of adjusting the content, all you need to do is log into the WordPress backend and make the changes there. No copy or extra installation is necessary. Here are a few introductory videos on editorial work with WordPress: https://learn.wordpress.org/learning-pathway/user/
If you want to make changes to the styling or actual programming, I would recommend creating a copy of the project. There are also various ways to do this, depending on your specific skills and requirements. One option would be to use the WP Staging plugin to create a copy of the project in the hosting itself. You can then make adjustments and test them in the copy and then restore the result. Or you can actually install a development environment locally. Again, this depends on your local capabilities. You can set up WordPress via Docker, in a virtual machine, or with localwp. It’s entirely up to you. To copy the project there, there are various plugins that enable migration, see:
If you actually want to program, the developer manual would be a good place to start: https://de.wordpress.org/plugins/search/migrate/
If WordPress is completely new to you, I would at least recommend that you don’t start working on the finished project straight away, but familiarize yourself with it first. The Playground is also helpful for getting a feel for the interface and seeing how things work: https://playground.wordpress.net/
