Allow specifying libcxx builder image. (#110303)

This change attempts to shift the libc++ builders over to new backend
infrastructure that allows running an arbitrary container for the
libc++ job.

This has been a long time in the making, and support from github
and gke is finally at the point where it's possible (hopefully).

This change should also demonstrate another important property:
No Downtime Upgrades.

If this goes well, we'll be able to test the upgrade as a part
of the PR process, and then commiting it to main should (ideally)
not break anything.

.github/workflows/libcxx-build-and-test.yaml

diff --git a/.github/workflows/libcxx-build-and-test.yaml b/.github/workflows/libcxx-build-and-test.yaml
index 657e7f1..15d2957 100644
--- a/.github/workflows/libcxx-build-and-test.yaml
+++ b/.github/workflows/libcxx-build-and-test.yaml
@@ -49,7 +49,8 @@
 jobs:
   stage1:
     if: github.repository_owner == 'llvm'
-    runs-on: libcxx-runners-8-set
+    runs-on: libcxx-runners-set
+    container: ghcr.io/libcxx/actions-builder:testing-2024-09-21
     continue-on-error: false
     strategy:
       fail-fast: false
@@ -85,7 +86,8 @@
             **/crash_diagnostics/*
   stage2:
     if: github.repository_owner == 'llvm'
-    runs-on: libcxx-runners-8-set
+    runs-on: libcxx-runners-set
+    container: ghcr.io/libcxx/actions-builder:testing-2024-09-21
     needs: [ stage1 ]
     continue-on-error: false
     strategy:
@@ -162,20 +164,21 @@
           'benchmarks',
           'bootstrapping-build'
         ]
-        machine: [ 'libcxx-runners-8-set' ]
+        machine: [ 'libcxx-runners-set' ]
         include:
         - config: 'generic-cxx26'
-          machine: libcxx-runners-8-set
+          machine: libcxx-runners-set
         - config: 'generic-asan'
-          machine: libcxx-runners-8-set
+          machine: libcxx-runners-set
         - config: 'generic-tsan'
-          machine: libcxx-runners-8-set
+          machine: libcxx-runners-set
         - config: 'generic-ubsan'
-          machine: libcxx-runners-8-set
+          machine: libcxx-runners-set
         # Use a larger machine for MSAN to avoid timeout and memory allocation issues.
         - config: 'generic-msan'
-          machine: libcxx-runners-8-set
+          machine: libcxx-runners-set
     runs-on: ${{ matrix.machine }}
+    container: ghcr.io/libcxx/actions-builder:testing-2024-09-21
     steps:
       - uses: actions/checkout@v4
       - name: ${{ matrix.config }}