repo: promote app-next to main example app

This renames packages to make the new frontend system the default:

- packages/app → packages/app-legacy (example-app-legacy)
- packages/app-next → packages/app (example-app)
- packages/app-next-example-plugin → packages/app-example-plugin

Updated all related configuration, scripts, and documentation.

Signed-off-by: Patrik Oldsberg <poldsberg@gmail.com>
Co-authored-by: Cursor <cursoragent@cursor.com>
Signed-off-by: Patrik Oldsberg <poldsberg@gmail.com>
Co-authored-by: Cursor <cursoragent@cursor.com>
Signed-off-by: Patrik Oldsberg <poldsberg@gmail.com>
Co-authored-by: Cursor <cursoragent@cursor.com>
Signed-off-by: Patrik Oldsberg <poldsberg@gmail.com>
Co-authored-by: Cursor <cursoragent@cursor.com>

docs/features/search/declarative-integration.md

@@ -25,7 +25,7 @@ The search plugin is a collection of extensions that implement the search featur
 
 ### Installation
 
-Only one step is required to start using the `Search` plugin within declarative integration, so all you have to do is to install the `@backstage/plugin-catalog` and `@backstage/plugin-search` packages, (e.g., [app-next](https://github.com/backstage/backstage/tree/master/packages/app-next)):
+Only one step is required to start using the `Search` plugin within declarative integration, so all you have to do is to install the `@backstage/plugin-catalog` and `@backstage/plugin-search` packages, (e.g., [app](https://github.com/backstage/backstage/tree/master/packages/app)):
 
 ```sh
 yarn add @backstage/plugin-catalog @backstage/plugin-search

docs/frontend-system/index.md

@@ -9,4 +9,4 @@ description: The Frontend System
 
 We recommend migrating your frontend plugins to the new frontend system. If you do please do so under an `/alpha` sub-path export.
 
-You can find an example app setup in the [`app-next` package](https://github.com/backstage/backstage/tree/master/packages/app-next).
+You can find an example app setup in the [`app` package](https://github.com/backstage/backstage/tree/master/packages/app).