[libc++] Add a Github action to build libc++'s Docker images (#110020)

This patch adds a Github action that runs whenever changes to the libc++
Docker images are pushed to `main`. The action will rebuild the Docker
images and push them to LLVM's container registry so that we can then
point to those images from our CI nodes.

.github/workflows/libcxx-build-containers.yml

@@ -0,0 +1,63 @@
+# This file defines an action that builds the various Docker images used to run
+# libc++ CI whenever modifications to those Docker files are pushed to `main`.
+#
+# The images are pushed to the LLVM package registry at https://github.com/orgs/llvm/packages
+# and tagged appropriately. The selection of which Docker image version is used by the libc++
+# CI nodes at any given point is controlled from the workflow files themselves.
+
+name: Build Docker images for libc++ CI
+
+permissions:
+  contents: read
+  packages: write
+
+on:
+  push:
+    branches:
+      - main
+    paths:
+      - 'libcxx/utils/ci/**'
+      - '.github/workflows/libcxx-build-containers.yml'
+  pull_request:
+    branches:
+      - main
+    paths:
+      - 'libcxx/utils/ci/**'
+      - '.github/workflows/libcxx-build-containers.yml'
+
+jobs:
+  build-and-push:
+    runs-on: ubuntu-latest
+    if: github.repository_owner == 'llvm'
+
+    steps:
+    - uses: actions/checkout@v4
+
+    - name: Build the Linux builder image and the Android builder image
+      working-directory: libcxx/utils/ci
+      run:
+        - docker compose build actions-builder
+        - docker compose build android-buildkite-builder
+
+    - name: Log in to GitHub Container Registry
+      uses: docker/login-action@v3
+      with:
+        registry: ghcr.io
+        username: ${{ github.actor }}
+        password: ${{ secrets.GITHUB_TOKEN }}
+
+    - name: Push the Linux builder image
+      if: github.event_name == 'push'
+      working-directory: libcxx/utils/ci
+      run:
+        - docker compose push actions-builder
+      env:
+        TAG: libcxx-linux-builder:${{ github.sha }}
+
+    - name: Push the Android builder image
+      if: github.event_name == 'push'
+      working-directory: libcxx/utils/ci
+      run:
+        - docker compose push android-buildkite-builder
+      env:
+        TAG: libcxx-android-builder:${{ github.sha }}