Sorry for the late answer.
I don’t see the search box on the given site, there is an inscription “Your access to this site has been limited by the site owner”.
Unfortunately, all themes contain different CSSs, which sometimes override google’s CSS settings. There is no general solution, site designers can correct this by creating custom CSSs for the specific theme. Alternatively, try setting the “Use default corrections CSS v2” checkbox on the “WP Google Search” settings page.
The setting values are not necessarily deleted by the plugins, I have looked at some plugin now and only one deleted its own settings. So it is normal for the settings to be retained. Clearing the settings would not solve the problem.
Please help me how to test the search box on your page.