ci/docker: unify image build logic and run virgin tests across all distros

Refactor Dockerfile into multi-stage virgin/full targets and introduce a single
flag-based image build script. Standardize image naming, remove redundant build
scripts, and update Makefile targets accordingly. CI workflows now build missing
virgin images and run root and user tests consistently across all supported
distributions.

https://chatgpt.com/share/693c29d9-9b28-800f-a549-5661c783d968

.github/workflows/test-virgin-root.yml

@@ -7,6 +7,10 @@ jobs:
   test-virgin-root:
     runs-on: ubuntu-latest
     timeout-minutes: 45
+    strategy:
+      fail-fast: false
+      matrix:
+        distro: [arch, debian, ubuntu, fedora, centos]
 
     steps:
       - name: Checkout repository
@@ -15,7 +19,14 @@ jobs:
       - name: Show Docker version
         run: docker version
 
-      - name: Virgin Arch pkgmgr flake test (root)
+      # 🔹 BUILD virgin image if missing
+      - name: Build virgin container (${{ matrix.distro }})
+        run: |
+          set -euo pipefail
+          distro="${{ matrix.distro }}" make build-missing
+
+      # 🔹 RUN test inside virgin image
+      - name: Virgin ${{ matrix.distro }} pkgmgr test (root)
         run: |
           set -euo pipefail
 
@@ -24,13 +35,10 @@ jobs:
             -v pkgmgr_repos:/root/Repositories \
             -v pkgmgr_pip_cache:/root/.cache/pip \
             -w /src \
-            archlinux:latest \
+            "pkgmgr-${{ matrix.distro }}-virgin" \
             bash -lc '
               set -euo pipefail
 
-              pacman -Syu --noconfirm git python python-pip nix make
-
-              # Fix: allow git operations on mounted repo path
               git config --global --add safe.directory /src
 
               make install
@@ -46,4 +54,3 @@ jobs:
               echo ">>> Running Nix-based: nix run .#pkgmgr -- version pkgmgr"
               nix run /src#pkgmgr -- version pkgmgr
             '
-