WordPress style.css not updating, only after theme reload

The proper way to add a style, as in a template or in a theme, is to use the wp_enqueue_style function. See https://developer.wordpress.org/reference/functions/wp_enqueue_style/ .

One of the parameters in the function is a version number, which you can change if you make changes to the CSS in the file. That will force WP into loading the new version, and not to use a cached version of the file.