Support basePath with edge runtime for Custom App Routes (#52910)

Fixes a bug where the edge runtime didn't support `basePath` with Custom App Routes.

- Fixes #49661

packages/next/src/server/web/edge-route-module-wrapper.ts

@@ -4,11 +4,12 @@ import type { RouteModule } from '../future/route-modules/route-module'
 import type { NextRequest } from './spec-extension/request'
 
 import './globals'
+
 import { adapter, type AdapterOptions } from './adapter'
 import { IncrementalCache } from '../lib/incremental-cache'
-
-import { removeTrailingSlash } from '../../shared/lib/router/utils/remove-trailing-slash'
 import { RouteMatcher } from '../future/route-matchers/route-matcher'
+import { removeTrailingSlash } from '../../shared/lib/router/utils/remove-trailing-slash'
+import { removePathPrefix } from '../../shared/lib/router/utils/remove-path-prefix'
 
 type WrapOptions = Partial<Pick<AdapterOptions, 'page'>>
 
@@ -64,7 +65,14 @@ export class EdgeRouteModuleWrapper {
   private async handler(request: NextRequest): Promise<Response> {
     // Get the pathname for the matcher. Pathnames should not have trailing
     // slashes for matching.
-    const pathname = removeTrailingSlash(new URL(request.url).pathname)
+    let pathname = removeTrailingSlash(new URL(request.url).pathname)
+
+    // Get the base path and strip it from the pathname if it exists.
+    const { basePath } = request.nextUrl
+    if (basePath) {
+      // If the path prefix doesn't exist, then this will do nothing.
+      pathname = removePathPrefix(pathname, basePath)
+    }
 
     // Get the match for this request.
     const match = this.matcher.match(pathname)

test/e2e/app-dir/app-routes/app-custom-route-base-path.test.ts

@@ -0,0 +1,2 @@
+process.env.BASE_PATH = '/docs'
+require('./app-custom-routes.test')