Add cachix to action

Author: TymanWasTaken

.github/workflows/push.yaml

@@ -29,12 +29,22 @@ jobs:
                   purge-last-accessed: 0
                   purge-primary-key: never
 
+            - uses: cachix/cachix-action@v15
+              with:
+                  name: polyfrost
+                  authToken: "${{ secrets.CACHIX_AUTH_TOKEN }}"
+                  signingKey: "${{ secrets.CACHIX_SIGNING_KEY }}"
+                  skipPush: true
+
             - name: Check nix flake
               run: nix -L flake check --keep-going
 
             - name: Build backend with nix
               run: nix -L build .#backend
 
+            - name: Push to Cachix
+              run: cachix push polyfrost ./result
+
             - name: Upload built nix package
               uses: actions/upload-artifact@v4
               with: