nix: Refactor gh-actions and re-enable nightly builds (#31489)

Now that the nix build is working again, re-enable nightly builds and
refactor the workflow for re-use between nightly releases and CI jobs.

Release Notes:

- N/A

---------

Co-authored-by: Rahul Butani <rrbutani@users.noreply.github.com>

flake.lock

@@ -2,11 +2,11 @@
   "nodes": {
     "crane": {
       "locked": {
-        "lastModified": 1742394900,
-        "narHash": "sha256-vVOAp9ahvnU+fQoKd4SEXB2JG2wbENkpqcwlkIXgUC0=",
+        "lastModified": 1748047550,
+        "narHash": "sha256-t0qLLqb4C1rdtiY8IFRH5KIapTY/n3Lqt57AmxEv9mk=",
         "owner": "ipetkov",
         "repo": "crane",
-        "rev": "70947c1908108c0c551ddfd73d4f750ff2ea67cd",
+        "rev": "b718a78696060df6280196a6f992d04c87a16aef",
         "type": "github"
       },
       "original": {
@@ -17,11 +17,11 @@
     },
     "flake-compat": {
       "locked": {
-        "lastModified": 1733328505,
-        "narHash": "sha256-NeCCThCEP3eCl2l/+27kNNK7QrwZB1IJCrXfrbv5oqU=",
+        "lastModified": 1747046372,
+        "narHash": "sha256-CIVLLkVgvHYbgI2UpXvIIBJ12HWgX+fjA8Xf8PUmqCY=",
         "owner": "edolstra",
         "repo": "flake-compat",
-        "rev": "ff81ac966bb2cae68946d5ed5fc4994f96d0ffec",
+        "rev": "9100a0f413b0c601e0533d1d94ffd501ce2e7885",
         "type": "github"
       },
       "original": {
@@ -33,10 +33,10 @@
     "nixpkgs": {
       "locked": {
         "lastModified": 315532800,
-        "narHash": "sha256-kgy4FnRFGj62QO3kI6a6glFl8XUtKMylWGybnVCvycM=",
-        "rev": "b3582c75c7f21ce0b429898980eddbbf05c68e55",
+        "narHash": "sha256-3c6Axl3SGIXCixGtpSJaMXLkkSRihHDlLaGewDEgha0=",
+        "rev": "3108eaa516ae22c2360928589731a4f1581526ef",
         "type": "tarball",
-        "url": "https://releases.nixos.org/nixpkgs/nixpkgs-25.05pre796313.b3582c75c7f2/nixexprs.tar.xz?rev=b3582c75c7f21ce0b429898980eddbbf05c68e55"
+        "url": "https://releases.nixos.org/nixpkgs/nixpkgs-25.11pre806109.3108eaa516ae/nixexprs.tar.xz"
       },
       "original": {
         "type": "tarball",
@@ -58,11 +58,11 @@
         ]
       },
       "locked": {
-        "lastModified": 1747363019,
-        "narHash": "sha256-N4dwkRBmpOosa4gfFkFf/LTD8oOcNkAyvZ07JvRDEf0=",
+        "lastModified": 1748227081,
+        "narHash": "sha256-RLnN7LBxhEdCJ6+rIL9sbhjBVDaR6jG377M/CLP/fmE=",
         "owner": "oxalica",
         "repo": "rust-overlay",
-        "rev": "0e624f2b1972a34be1a9b35290ed18ea4b419b6f",
+        "rev": "1cbe817fd8c64a9f77ba4d7861a4839b0b15983e",
         "type": "github"
       },
       "original": {