Check the examples with a keyboard.
Never hide the focus styles. Navigating with a keyboard becomes very difficult. If you don't like the default focus styles, you can use your own focus styles as long as you make sure they are visible enough on all backgrounds.
Also, it is recommended to check also that high contrast mode can override your focus style. It's not required by the WCAG AA level at least yet, but try to avoid excluding your users even if it isn't mandatory to take them into account.