fix: Update workflow names and conditions for E2E tests

.gitea/workflows/build-and-push.yml

@@ -2,7 +2,7 @@ name: Build and Push Docker Image
 on:
   workflow_run:
     workflows:
-      - Run Tests
+      - Run E2E Tests
     branches:
       - main
     types:

.gitea/workflows/test-e2e.yml

@@ -1,17 +1,19 @@
 name: Run E2E Tests
 
 on:
-  push:
+  workflow_run:
-    branches:
+    workflows:
-      - '**'
+      - Run Tests
-  pull_request:
     branches:
       - main
+    types:
+      - completed
   workflow_dispatch:
 
 jobs:
   e2e:
     name: E2E Tests
+    if: ${{ github.event_name == 'workflow_dispatch' || (github.event_name == 'workflow_run' && github.event.workflow_run.conclusion == 'success') }}
     runs-on: ubuntu-latest
     container: mcr.microsoft.com/playwright/python:v1.55.0-jammy
     env:
@@ -47,7 +49,14 @@ jobs:
           curl -fsSL https://deb.nodesource.com/setup_20.x | bash -
           apt-get install -y nodejs
 
-      - name: Checkout code
+      - name: Checkout code (workflow_run)
+        if: ${{ github.event_name == 'workflow_run' }}
+        uses: actions/checkout@v4
+        with:
+          ref: ${{ github.event.workflow_run.head_sha }}
+
+      - name: Checkout code (manual)
+        if: ${{ github.event_name != 'workflow_run' }}
         uses: actions/checkout@v4
 
       - name: Export PYTHONPATH