Update QA specs for Run Pipeline form

What does this MR do and why?

Updates QA tests to address the following issues:

• #375552 (closed)
• #378249 (closed)
• #378250 (closed)

Screenshots or screen recordings

N/A

How to set up and validate locally

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• I have evaluated the MR acceptance checklist for this MR.

qa/qa/specs/features/browser_ui/4_verify/ci_variable/custom_variable_spec.rb

 # frozen_string_literal: true
 
 module QA
-  RSpec.describe 'Verify', :runner, product_group: :pipeline_authoring do
-    describe 'Pipeline with customizable variable' do
+  RSpec.describe 'Verify', :runner do
+    describe 'Pipeline with customizable variable', feature_flag: {
+      name: :run_pipeline_graphql,
+      scope: :global
+    } do
       let(:executor) { "qa-runner-#{Time.now.to_i}" }
       let(:pipeline_job_name) { 'customizable-variable' }
       let(:variable_custom_value) { 'Custom Foo' }
@@ -45,43 +48,66 @@ module QA
         end
       end
 
-      before do
-        Flow::Login.sign_in
-        project.visit!
-        Page::Project::Menu.perform(&:click_ci_cd_pipelines)
-        Page::Project::Pipeline::Index.perform do |index|
-          index.click_run_pipeline_button
-        end
-      end
+      shared_examples 'pipeline with custom variable' do
+        before do
+          Flow::Login.sign_in
 
-      after do
-        [runner, project].each(&:remove_via_api!)
-      end
+          project.visit!
+          Page::Project::Menu.perform(&:click_ci_cd_pipelines)
+          Page::Project::Pipeline::Index.perform(&:click_run_pipeline_button)
 
-      it(
-        'manually creates a pipeline and uses the defined custom variable value',
-        testcase: 'https://gitlab.com/gitlab-org/gitlab/-/quality/test_cases/361814'
-      ) do
-        Page::Project::Pipeline::New.perform do |new|
-          new.configure_variable(value: variable_custom_value)
-          new.click_run_pipeline_button
+          # Sometimes the variables will not be prefilled because of reactive cache
+          # So we revisit the page again
+          project.visit!
+          Page::Project::Menu.perform(&:click_ci_cd_pipelines)
+          Page::Project::Pipeline::Index.perform(&:click_run_pipeline_button)
         end
 
-        Page::Project::Pipeline::Show.perform do |show|
-          Support::Waiter.wait_until { show.passed? }
+        after do
+          [runner, project].each(&:remove_via_api!)
         end
 
-        job = Resource::Job.fabricate_via_api! do |job|
-          job.id = project.job_by_name(pipeline_job_name)[:id]
-          job.name = pipeline_job_name
-          job.project = project
+        it 'manually creates a pipeline and uses the defined custom variable value' do
+          Page::Project::Pipeline::New.perform do |new|
+            new.configure_variable(value: variable_custom_value)
+            new.click_run_pipeline_button
+          end
+
+          Page::Project::Pipeline::Show.perform do |show|
+            Support::Waiter.wait_until { show.passed? }
+          end
+
+          job = Resource::Job.fabricate_via_api! do |job|
+            job.id = project.job_by_name(pipeline_job_name)[:id]
+            job.name = pipeline_job_name
+            job.project = project
+          end
+
+          job.visit!
+
+          Page::Project::Job::Show.perform do |show|
+            expect(show.output).to have_content(variable_custom_value)
+          end
         end
+      end
+
+      # TODO: Clean up tests when run_pipeline_graphql is enabled
+      # Issue https://gitlab.com/gitlab-org/gitlab/-/issues/372310
+      context 'with feature flag disabled',
+        testcase: 'https://gitlab.com/gitlab-org/gitlab/-/quality/test_cases/361814' do
+        it_behaves_like 'pipeline with custom variable'
+      end
 
-        job.visit!
+      context 'with feature flag enabled' do
+        before do
+          Runtime::Feature.enable(:run_pipeline_graphql)
+        end
 
-        Page::Project::Job::Show.perform do |show|
-          expect(show.output).to have_content(variable_custom_value)
+        after do
+          Runtime::Feature.disable(:run_pipeline_graphql)
         end
+
+        it_behaves_like 'pipeline with custom variable'
       end
     end
   end