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>

.changeset/pre.json

@@ -2,10 +2,10 @@
   "mode": "pre",
   "tag": "next",
   "initialVersions": {
-    "example-app": "0.2.117",
+    "example-app-legacy": "0.2.117",
     "@backstage/app-defaults": "1.7.4",
-    "example-app-next": "0.0.31",
-    "app-next-example-plugin": "0.0.31",
+    "example-app": "0.0.31",
+    "app-example-plugin": "0.0.31",
     "example-backend": "0.0.46",
     "@backstage/backend-app-api": "1.4.1",
     "@backstage/backend-defaults": "0.15.0",

.changeset/repo-tools-app-rename.md

@@ -0,0 +1,5 @@
+---
+'@backstage/repo-tools': patch
+---
+
+Updated package-docs exclude list to reflect renamed example app packages.