How to make /category/ URL load properly instead of 404 error?

Yes, there is such way. To be precise, there are many ways to accomplish that.

You can add ‘Category’ page. Make sure that its slug is set to ‘category’. If you go to then this page will be shown. If there were no custom changes to rewrite rules, then WordPress will first try to match pages, and then categories, so it should work.

You can also remove category base from url. You can do this using some plugins (WP No Category Base – WPML compatible is one of plugins you could use).