Stabilize issue-project e2e test, increase timeout factor (#37297)

1. stabilize flaky e2e test from
2f5b5a9e9c
2. increase ci timeout factor to 4 as 3 was not enough
3. add a `e2e` category to files-changed so e2e-test-only changes
trigger ci

---
This PR was written with the help of Claude Opus 4.7

---------

Co-authored-by: Claude (Opus 4.7) <noreply@anthropic.com>

.github/workflows/files-changed.yml

@@ -21,6 +21,8 @@ on:
         value: ${{ jobs.detect.outputs.yaml }}
       json:
         value: ${{ jobs.detect.outputs.json }}
+      e2e:
+        value: ${{ jobs.detect.outputs.e2e }}
 
 jobs:
   detect:
@@ -38,6 +40,7 @@ jobs:
       swagger: ${{ steps.changes.outputs.swagger }}
       yaml: ${{ steps.changes.outputs.yaml }}
       json: ${{ steps.changes.outputs.json }}
+      e2e: ${{ steps.changes.outputs.e2e }}
     steps:
       - uses: actions/checkout@v6
       - uses: dorny/paths-filter@v4
@@ -107,3 +110,8 @@ jobs:
 
             json:
               - "**/*.json"
+
+            e2e:
+              - "tests/e2e/**"
+              - "tools/test-e2e.sh"
+              - "playwright.config.ts"

.github/workflows/pull-e2e-tests.yml

@@ -14,7 +14,7 @@ jobs:
       contents: read
 
   test-e2e:
-    if: needs.files-changed.outputs.backend == 'true' || needs.files-changed.outputs.frontend == 'true'
+    if: needs.files-changed.outputs.backend == 'true' || needs.files-changed.outputs.frontend == 'true' || needs.files-changed.outputs.e2e == 'true'
     needs: files-changed
     runs-on: ubuntu-latest
     permissions: