Fix optimized url helpers when using relative url root

Fixes #31220.

(cherry picked from commit 00c0e400)

actionpack/CHANGELOG.md

+*   Fix optimized url helpers when using relative url root
+
+    Fixes #31220.
+
+    *Andrew White*
+
 *   Ensure dev and prod puma configs do not clobber `ActionDispatch::SystemTesting` defaults. Adds workers: 0 and daemon: false
 
     *Max Schwenk*

actionpack/lib/action_dispatch/routing/route_set.rb

@@ -203,6 +203,16 @@ def call(t, args, inner_options)
               if args.size == arg_size && !inner_options && optimize_routes_generation?(t)
                 options = t.url_options.merge @options
                 options[:path] = optimized_helper(args)
+
+                original_script_name = options.delete(:original_script_name)
+                script_name = t._routes.find_script_name(options)
+
+                if original_script_name
+                  script_name = original_script_name + script_name
+                end
+
+                options[:script_name] = script_name
+
                 url_strategy.call options
               else
                 super

actionpack/test/dispatch/routing_test.rb

@@ -5051,3 +5051,40 @@ def recognize_path(*args)
       Routes.recognize_path(*args)
     end
 end
+
+class TestRelativeUrlRootGeneration < ActionDispatch::IntegrationTest
+  config = ActionDispatch::Routing::RouteSet::Config.new("/blog", false)
+
+  stub_controllers(config) do |routes|
+    Routes = routes
+
+    routes.draw do
+      get "/", to: "posts#index", as: :posts
+      get "/:id", to: "posts#show", as: :post
+    end
+  end
+
+  include Routes.url_helpers
+
+  APP = build_app Routes
+
+  def app
+    APP
+  end
+
+  def test_url_helpers
+    assert_equal "/blog/", posts_path({})
+    assert_equal "/blog/", Routes.url_helpers.posts_path({})
+
+    assert_equal "/blog/1", post_path(id: "1")
+    assert_equal "/blog/1", Routes.url_helpers.post_path(id: "1")
+  end
+
+  def test_optimized_url_helpers
+    assert_equal "/blog/", posts_path
+    assert_equal "/blog/", Routes.url_helpers.posts_path
+
+    assert_equal "/blog/1", post_path("1")
+    assert_equal "/blog/1", Routes.url_helpers.post_path("1")
+  end
+end