How can we center logo with navigation divided on both sides?

this is out of scope for us as Cache plugins can cause issues that are impossible for us to diagnose. Whether they be conflicts with other plugins, HTAccess issues etc. But These are the settings that are used on GeneratePress:

https://generatepress.com/fastest-wordpress-theme/

And no issues here.
If need be under the CSS settings you have an option to exclude, you could add the style.css to this and see if that helps.