ci: run build, test, lint and format as nix flake checks

Adopt kradalby/flake-checks: flake.nix exposes build, gotest,
golangci-lint and formatting checks over one shared, fileset-filtered
source set, and nix-checks.yml gates each with
nix build .#checks.<system>.<name>. Drop test.yml and lint.yml —
gotestsum, golangci-lint and prettier are now those checks. golangci-lint
runs full-tree; Go formatting stays in it while formatting adds prettier.

hscontrol/servertest is too slow and timing-sensitive for the sandboxed
gotest check, so servertest.yml runs it in the devShell instead.

flake.lock

@@ -1,5 +1,27 @@
 {
   "nodes": {
+    "flake-checks": {
+      "inputs": {
+        "flake-utils": "flake-utils",
+        "nixpkgs": [
+          "nixpkgs"
+        ],
+        "treefmt-nix": "treefmt-nix"
+      },
+      "locked": {
+        "lastModified": 1781951072,
+        "narHash": "sha256-hA9u6hB4QzpReP8hudxqiaa4vLhoRvtXi6YmUgJRGEs=",
+        "owner": "kradalby",
+        "repo": "flake-checks",
+        "rev": "3d2882efec5cf10f8b5a8a035d93ba6ba9f21717",
+        "type": "github"
+      },
+      "original": {
+        "owner": "kradalby",
+        "repo": "flake-checks",
+        "type": "github"
+      }
+    },
     "flake-utils": {
       "inputs": {
         "systems": "systems"
@@ -18,6 +40,24 @@
         "type": "github"
       }
     },
+    "flake-utils_2": {
+      "inputs": {
+        "systems": "systems_2"
+      },
+      "locked": {
+        "lastModified": 1731533236,
+        "narHash": "sha256-l0KFg5HjrsfsO/JpG+r7fRrqm12kzFHyUHqHCVpMMbI=",
+        "owner": "numtide",
+        "repo": "flake-utils",
+        "rev": "11707dc2f618dd54ca8739b309ec4fc024de578b",
+        "type": "github"
+      },
+      "original": {
+        "owner": "numtide",
+        "repo": "flake-utils",
+        "type": "github"
+      }
+    },
     "nixpkgs": {
       "locked": {
         "lastModified": 1781153106,
@@ -36,7 +76,8 @@
     },
     "root": {
       "inputs": {
-        "flake-utils": "flake-utils",
+        "flake-checks": "flake-checks",
+        "flake-utils": "flake-utils_2",
         "nixpkgs": "nixpkgs"
       }
     },
@@ -54,6 +95,42 @@
         "repo": "default",
         "type": "github"
       }
+    },
+    "systems_2": {
+      "locked": {
+        "lastModified": 1681028828,
+        "narHash": "sha256-Vy1rq5AaRuLzOxct8nz4T6wlgyUR7zLU309k9mBC768=",
+        "owner": "nix-systems",
+        "repo": "default",
+        "rev": "da67096a3b9bf56a91d16901293e51ba5b49a27e",
+        "type": "github"
+      },
+      "original": {
+        "owner": "nix-systems",
+        "repo": "default",
+        "type": "github"
+      }
+    },
+    "treefmt-nix": {
+      "inputs": {
+        "nixpkgs": [
+          "flake-checks",
+          "nixpkgs"
+        ]
+      },
+      "locked": {
+        "lastModified": 1780220602,
+        "narHash": "sha256-eynAfOmbmxJnkp7YewvCEbShNnnYJ9gLLqkzsYtBPeM=",
+        "owner": "numtide",
+        "repo": "treefmt-nix",
+        "rev": "db947814a175b7ca6ded66e21383d938df01c227",
+        "type": "github"
+      },
+      "original": {
+        "owner": "numtide",
+        "repo": "treefmt-nix",
+        "type": "github"
+      }
     }
   },
   "root": "root",