Composer is an excellent way of managing dependencies but in order to use it properly it does require a build and deployment process.
The two ways of deploying a site built with composer is to either generate an artefact with the composer dependencies installed, or to install composer as part of the deployment process. Both of these approaches require not committing the vendor directory and other third party libraries (like Drupal core for example) to the git repository.
Many developers tend to go for the approach of committing the composer dependencies to the repository in order to simplify their workflow. This approach, while simple, does have its problems. I have talked about the problems of committing the composer vendor directory in detail in a previous article.
Read more here: https://www.hashbangcode.com/article/drupal-9-deleting-and-ignoring-drupal-composer-directories-git