refactor(nix): use flake-parts and flake-compat

- redefine `{default,shell}.nix` to derive from `flake.nix` (using
  `flake-compat`)
- use `flake-parts`' `_module.args.pkgs` machinery to apply overlays
  (instead of `pkgsFor`)
- extract `homeManagerModule` to `nix/module.nix`
- rename package at `nix/default.nix` to `nix/package.nix`

Co-authored-by: reo101 <pavel.atanasov2001@gmail.com>

flake.lock

@@ -15,6 +15,39 @@
         "type": "github"
       }
     },
+    "flake-compat": {
+      "locked": {
+        "lastModified": 1733328505,
+        "narHash": "sha256-NeCCThCEP3eCl2l/+27kNNK7QrwZB1IJCrXfrbv5oqU=",
+        "owner": "edolstra",
+        "repo": "flake-compat",
+        "rev": "ff81ac966bb2cae68946d5ed5fc4994f96d0ffec",
+        "type": "github"
+      },
+      "original": {
+        "owner": "edolstra",
+        "repo": "flake-compat",
+        "type": "github"
+      }
+    },
+    "flake-parts": {
+      "inputs": {
+        "nixpkgs-lib": "nixpkgs-lib"
+      },
+      "locked": {
+        "lastModified": 1743550720,
+        "narHash": "sha256-hIshGgKZCgWh6AYJpJmRgFdR3WUbkY04o82X05xqQiY=",
+        "owner": "hercules-ci",
+        "repo": "flake-parts",
+        "rev": "c621e8422220273271f52058f618c94e405bb0f5",
+        "type": "github"
+      },
+      "original": {
+        "owner": "hercules-ci",
+        "repo": "flake-parts",
+        "type": "github"
+      }
+    },
     "naersk": {
       "inputs": {
         "nixpkgs": "nixpkgs"
@@ -49,6 +82,21 @@
         "type": "github"
       }
     },
+    "nixpkgs-lib": {
+      "locked": {
+        "lastModified": 1743296961,
+        "narHash": "sha256-b1EdN3cULCqtorQ4QeWgLMrd5ZGOjLSLemfa00heasc=",
+        "owner": "nix-community",
+        "repo": "nixpkgs.lib",
+        "rev": "e4822aea2a6d1cdd36653c134cacfd64c97ff4fa",
+        "type": "github"
+      },
+      "original": {
+        "owner": "nix-community",
+        "repo": "nixpkgs.lib",
+        "type": "github"
+      }
+    },
     "nixpkgs_2": {
       "locked": {
         "lastModified": 1745930157,
@@ -68,6 +116,8 @@
     "root": {
       "inputs": {
         "crane": "crane",
+        "flake-compat": "flake-compat",
+        "flake-parts": "flake-parts",
         "naersk": "naersk",
         "nixpkgs": "nixpkgs_2",
         "rust-overlay": "rust-overlay"