Add examples of apps with simplified UI

part of insightsengineering/teal.transform#24

Don't know yet where to put it, but we are in the middle of massively simplifying the `teal::init` API and it would be good to have a place where we highlight those changes.

The simplification I am talking about happened in:
* https://github.com/insightsengineering/teal/issues/51
* https://github.com/insightsengineering/teal/issues/49
but there are more issues about it and we could expand the new section with the new changes.

Applies to examples and vignettes

Review the repository's examples and vignettes, then read the linked teal issues 51 and 49 to understand the simplified teal::init API. Decide where a new section belongs and add examples that highlight the API changes; done means the relevant examples and vignettes clearly showcase simplified apps.

Written by the indexing model from the issue text.