Adopt iOS 15 style navigation bars

### Your use case

#### What would you like to do?
Following on from #5422 which enabled the new style for tab bars, it would be good to also enable this for navigation bars. The following should be done:

1. Remove the opaque appearance, ideally just tinting bars like we do for tab bars.
2. Start using UISearchController instead of manually adding search bars to the navigation bar's title view.
3. Update search bar appearances as necessary.
4. Check for visual glitches when pushing/popping and address these.

Additionally, we should then probably adopt the default header padding that was set to 0 in #5422 and investigate using either default or tinted header backgrounds.

Start by reviewing the implementation from #5422 that enabled the iOS 15 tab-bar style, then locate the navigation-bar appearance and manually added search-bar handling. Compare the navigation and search-bar behavior with the iOS 15 defaults, including push/pop transitions; done means the requested appearance changes work without visual glitches and header padding/background behavior has been investigated.

Written by the indexing model from the issue text.