chore: CI: restore cache in update-stage0 (#9179)

Avoid rebuilding stage 0 all the time

.github/workflows/build-template.yml

@@ -97,11 +97,11 @@ jobs:
           sudo apt-get update
           sudo apt-get install -y gcc-multilib g++-multilib ccache libuv1-dev:i386 pkgconf:i386
         if: matrix.cmultilib
-      - name: Cache
+      - name: Restore Cache
         id: restore-cache
         uses: actions/cache/restore@v4
         with:
-          # NOTE: must be in sync with `save` below
+          # NOTE: must be in sync with `save` below and with `restore-cache` in `update-stage0.yml`
           path: |
             .ccache
             ${{ matrix.name == 'Linux Lake' && false && 'build/stage1/**/*.trace

.github/workflows/update-stage0.yml

@@ -52,6 +52,18 @@ jobs:
       run: |
         echo "NPROC=$(nproc 2>/dev/null || sysctl -n hw.logicalcpu 2>/dev/null || echo 4)" >> $GITHUB_ENV
       shell: 'nix develop -c bash -euxo pipefail {0}'
+    - name: Restore Cache
+      if: env.should_update_stage0 == 'yes'
+      uses: actions/cache/restore@v4
+      with:
+        # NOTE: must be in sync with `restore-cache` in `build-template.yml`
+        # TODO: actually switch to USE_LAKE once it caches more; for now it just caches more often than any other build type so let's use its cache
+        path: |
+          .ccache
+        key: Linux Lake-build-v3-${{ github.sha }}
+        # fall back to (latest) previous cache
+        restore-keys: |
+          Linux Lake-build-v3
     - if: env.should_update_stage0 == 'yes'
       run: cmake --preset release
       shell: 'nix develop -c bash -euxo pipefail {0}'