fix: Update E2E test workflow conditions and branch ignore settings

.gitea/workflows/test-e2e.yml

@@ -1,6 +1,10 @@
 name: Run E2E Tests
 
 on:
+  push:
+    branches-ignore:
+      - main
+      - refs/heads/main
   workflow_run:
     workflows:
       - Run Tests
@@ -11,7 +15,10 @@ on:
 jobs:
   e2e:
     name: E2E Tests
-    if: ${{ github.event_name == 'workflow_dispatch' || (github.event_name == 'workflow_run' && github.event.workflow_run.conclusion == 'success' && (github.event.workflow_run.head_branch == 'main' || github.event.workflow_run.head_branch == 'refs/heads/main')) }}
+    if: ${{ github.event_name == 'workflow_dispatch' ||
+      github.event_name == 'push' ||
+      (github.event_name == 'workflow_run' && github.event.workflow_run.conclusion == 'success' &&
+      (github.event.workflow_run.head_branch == 'main' || github.event.workflow_run.head_branch == 'refs/heads/main')) }}
     runs-on: ubuntu-latest
     container: mcr.microsoft.com/playwright/python:v1.55.0-jammy
     env: