Solution 1: You can give a classname to your component and prefix every CSS rule with this classname. e.g. <CustomSelect>, which translates to <div className="custom-select">, which you can style by prefixing every rule with .custom-select. You put that in the index.css inside your folder CustomSelect to be easily editable when you need it.
Solution 2: Otherwise you could try to use CSS modules (Vite supports them out-of-the-box I think).
Solution 3: Otherwise you could try one of the many "CSS-in-JS" libraries like styled-components.
Personally I'm using the solution 1, did for more than a decade, works fine, scales well, nothing to install and learn, just old straightforward CSS.