ci: Run flake-regressions also with the newly built daemon

Runs the tests against the new daemon as well as the cli.

This more reliably shares the artifact (not relying directly on github
actions cache). We've seen github evict our caches super fast, so it would
be nice to move away from it entirely if possible.

(cherry picked from commit 6eebfe6274)

.github/workflows/ci.yml

@@ -287,13 +287,21 @@ jobs:
         with:
           repository: NixOS/flake-regressions-data
           path: flake-regressions/tests
-      - uses: ./.github/actions/install-nix-action
+      - name: Download installer tarball
+        uses: actions/download-artifact@v7
         with:
-          dogfood: ${{ github.event_name == 'workflow_dispatch' && inputs.dogfood || github.event_name != 'workflow_dispatch' }}
-          extra_nix_config:
-            experimental-features = nix-command flakes
-          github_token: ${{ secrets.GITHUB_TOKEN }}
-      - run: nix build -L --out-link ./new-nix && PATH=$(pwd)/new-nix/bin:$PATH MAX_FLAKES=25 flake-regressions/eval-all.sh
+          name: installer-linux
+          path: out
+      - name: Looking up the installer tarball URL
+        id: installer-tarball-url
+        run: |
+          echo "installer-url=file://$GITHUB_WORKSPACE/out" >> "$GITHUB_OUTPUT"
+      - uses: cachix/install-nix-action@4e002c8ec80594ecd40e759629461e26c8abed15 # v31.9.0
+        with:
+          install_url: ${{ format('{0}/install', steps.installer-tarball-url.outputs.installer-url) }}
+          install_options: ${{ format('--tarball-url-prefix {0}', steps.installer-tarball-url.outputs.installer-url) }}
+      - name: Run flake regressions tests
+        run: MAX_FLAKES=25 flake-regressions/eval-all.sh
 
   profile_build:
     needs: tests