Fix page folder being wrongly resolved as page file (#42348)

Closes #42010.

## Bug

- [ ] Related issues linked using `fixes #number`
- [x] Integration tests added
- [ ] Errors have a helpful link attached, see `contributing.md`

## Feature

- [ ] Implements an existing feature request or RFC. Make sure the
feature request has been accepted for implementation before opening a
PR.
- [ ] Related issues linked using `fixes #number`
- [ ] Integration tests added
- [ ] Documentation added
- [ ] Telemetry added. In case of a feature if it's used or not.
- [ ] Errors have a helpful link attached, see `contributing.md`

## Documentation / Examples

- [ ] Make sure the linting passes by running `pnpm build && pnpm lint`
- [ ] The "examples guidelines" are followed from [our contributing
doc](https://github.com/vercel/next.js/blob/canary/contributing/examples/adding-examples.md)

packages/next/build/webpack/loaders/next-app-loader.ts

@@ -17,6 +17,8 @@ export const FILE_TYPES = {
   'not-found': 'not-found',
 } as const
 
+const PAGE_SEGMENT = 'page$'
+
 // TODO-APP: check if this can be narrowed.
 type ComponentModule = () => any
 export type ComponentsType = {
@@ -59,10 +61,8 @@ async function createTreeCodeFromPath({
     }
 
     for (const [parallelKey, parallelSegment] of parallelSegments) {
-      const parallelSegmentPath = segmentPath + '/' + parallelSegment
-
-      if (parallelSegment === 'page') {
-        const matchedPagePath = `${appDirPrefix}${parallelSegmentPath}`
+      if (parallelSegment === PAGE_SEGMENT) {
+        const matchedPagePath = `${appDirPrefix}${segmentPath}/page`
         const resolvedPagePath = await resolve(matchedPagePath)
         if (resolvedPagePath) pages.push(resolvedPagePath)
 
@@ -73,6 +73,7 @@ async function createTreeCodeFromPath({
         continue
       }
 
+      const parallelSegmentPath = segmentPath + '/' + parallelSegment
       const subtree = await createSubtreePropsFromSegmentPath([
         ...segments,
         parallelSegment,
@@ -175,12 +176,18 @@ const nextAppLoader: webpack.LoaderDefinitionFunction<{
     const matched: Record<string, string> = {}
     for (const path of normalizedAppPaths) {
       if (path.startsWith(pathname + '/')) {
-        const restPath = path.slice(pathname.length + 1)
+        const rest = path.slice(pathname.length + 1).split('/')
+
+        let matchedSegment = rest[0]
+        // It is the actual page, mark it sepcially.
+        if (rest.length === 1 && matchedSegment === 'page') {
+          matchedSegment = PAGE_SEGMENT
+        }
 
-        const matchedSegment = restPath.split('/')[0]
         const matchedKey = matchedSegment.startsWith('@')
           ? matchedSegment.slice(1)
           : 'children'
+
         matched[matchedKey] = matchedSegment
       }
     }

test/e2e/app-dir/app/app/dashboard/page/page.jsx

@@ -0,0 +1,7 @@
+export default function DashboardPagePage() {
+  return (
+    <>
+      <p>hello dashboard/page!</p>
+    </>
+  )
+}

test/e2e/app-dir/index.test.ts

@@ -292,6 +292,11 @@ describe('app dir', () => {
       )
     })
 
+    it('should serve page as a segment name correctly', async () => {
+      const html = await renderViaHTTP(next.url, '/dashboard/page')
+      expect(html).toContain('hello dashboard/page!')
+    })
+
     it('should include document html and body', async () => {
       const html = await renderViaHTTP(next.url, '/dashboard')
       const $ = cheerio.load(html)