ci: add nix flake and use in CI

Using system tooling can lead to weird behavior of available Node
versions, for example this IPv6 resolution error:
```
[3/5] Fetching packages...
error Error: connect EHOSTUNREACH 2606:4700::6810:1922:443
    at TCPConnectWrap.afterConnect [as oncomplete] (node:net:1495:16)
```

flake.lock

@@ -0,0 +1,26 @@
+{
+  "nodes": {
+    "nixpkgs": {
+      "locked": {
+        "lastModified": 1754028485,
+        "narHash": "sha256-IiiXB3BDTi6UqzAZcf2S797hWEPCRZOwyNThJIYhUfk=",
+        "owner": "NixOS",
+        "repo": "nixpkgs",
+        "rev": "59e69648d345d6e8fef86158c555730fa12af9de",
+        "type": "github"
+      },
+      "original": {
+        "id": "nixpkgs",
+        "ref": "nixos-25.05",
+        "type": "indirect"
+      }
+    },
+    "root": {
+      "inputs": {
+        "nixpkgs": "nixpkgs"
+      }
+    }
+  },
+  "root": "root",
+  "version": 7
+}