Use fenix toolchain in nix shell (#18227)

In #17974 we explicitly depend on rustc/cargo for the nix devShell,
however the fenix overlay that contains the latest stable versions was
not being applied to that shell. This led to the shell inheriting
whatever rustc/cargo was on nixos-unstable from nixpkgs, which sometimes
lags behind. This change fixes that, and also restructures the flake to
ensure that all outputs rely on the overlaid `pkgs`.

Release Notes:

- N/A

flake.lock

@@ -2,11 +2,11 @@
   "nodes": {
     "crane": {
       "locked": {
-        "lastModified": 1725409566,
-        "narHash": "sha256-PrtLmqhM6UtJP7v7IGyzjBFhbG4eOAHT6LPYOFmYfbk=",
+        "lastModified": 1727060013,
+        "narHash": "sha256-/fC5YlJy4IoAW9GhkJiwyzk0K/gQd9Qi4rRcoweyG9E=",
         "owner": "ipetkov",
         "repo": "crane",
-        "rev": "7e4586bad4e3f8f97a9271def747cf58c4b68f3c",
+        "rev": "6b40cc876c929bfe1e3a24bf538ce3b5622646ba",
         "type": "github"
       },
       "original": {
@@ -23,11 +23,11 @@
         "rust-analyzer-src": "rust-analyzer-src"
       },
       "locked": {
-        "lastModified": 1726813972,
-        "narHash": "sha256-t6turZgoSAVgj7hn5mxzNlLOeVeZvymFo8+ymB52q34=",
+        "lastModified": 1727073227,
+        "narHash": "sha256-1kmkEQmFfGVuPBasqSZrNThqyMDV1SzTalQdRZxtDRs=",
         "owner": "nix-community",
         "repo": "fenix",
-        "rev": "251caeafc75b710282ee7e375800f75f4c8c5727",
+        "rev": "88cc292eb3c689073c784d6aecc0edbd47e12881",
         "type": "github"
       },
       "original": {
@@ -53,11 +53,11 @@
     },
     "nixpkgs": {
       "locked": {
-        "lastModified": 1726642912,
-        "narHash": "sha256-wiZzKGHRAhItEuoE599Wm3ic+Lg/NykuBvhb+awf7N8=",
+        "lastModified": 1726937504,
+        "narHash": "sha256-bvGoiQBvponpZh8ClUcmJ6QnsNKw0EMrCQJARK3bI1c=",
         "owner": "NixOS",
         "repo": "nixpkgs",
-        "rev": "395c52d142ec1df377acd67db6d4a22950b02a98",
+        "rev": "9357f4f23713673f310988025d9dc261c20e70c6",
         "type": "github"
       },
       "original": {