Refactor test pipeline: introduce separate unit/e2e workflows, fix Dockerfile, update Makefile test targets, and move integration tests to tests/e2e.

Conversation reference:
https://chatgpt.com/share/69361e70-4d74-800f-acd7-51548ac3fa37

.github/workflows/test-e2e.yml

@@ -0,0 +1,25 @@
+name: Test package-manager (e2e)
+
+on:
+  push:
+    branches:
+      - main
+      - master
+      - develop
+      - "*"
+  pull_request:
+
+jobs:
+  test-e2e:
+    runs-on: ubuntu-latest
+    timeout-minutes: 60  # E2E + all distros can be heavier
+
+    steps:
+      - name: Checkout repository
+        uses: actions/checkout@v4
+
+      - name: Show Docker version
+        run: docker version
+
+      - name: Run E2E tests via make (all distros)
+        run: make test-e2e