core-api: remove deprecated registerRoute and deprecate addRoute

.changeset/proud-news-impress.md

@@ -0,0 +1,55 @@
+---
+'@backstage/core': minor
+---
+
+Removed deprecated `router.registerRoute` method in `createPlugin`.
+
+Deprecated `router.addRoute` method in `createPlugin`.
+
+Replace usage of the above two components with a routable extension.
+
+For example, given the following:
+
+```ts
+import { createPlugin } from '@backstage/core';
+import { MyPage } from './components/MyPage';
+import { rootRoute } from './routes';
+
+export const plugin = createPlugin({
+  id: 'my-plugin',
+  register({ router }) {
+    router.addRoute(rootRoute, MyPage);
+  },
+});
+```
+
+Migrate to
+
+```ts
+import { createPlugin, createRoutableExtension } from '@backstage/core';
+import { rootRoute } from './routes';
+
+export const plugin = createPlugin({
+  id: 'my-plugin',
+  routes: {
+    root: rootRoute,
+  },
+});
+
+export const MyPage = plugin.provide(
+  createRoutableExtension({
+    component: () => import('./components/MyPage').then(m => m.MyPage),
+    mountPoint: rootRoute,
+  }),
+);
+```
+
+And then use `MyPage` like this in the app:
+
+```tsx
+<FlatRoutes>
+...
+  <Route path='/my-path' element={<MyPage />}>
+...
+</FlatRoutes>
+```