test(nix): drive the installed binary through the shared tier (task 0038)

The Nix build now runs the installed-binary facet of the packaging tier
against the binary it has just produced, via an `installCheckPhase` that
sets `GITEA_AXI_INSTALLED_BIN` to `$out/bin/gitea-axi` and runs the new
`test:installed` script. Running after `fixupPhase` means the binary
under test is the wrapped one an operator actually gets, and naming it is
all the phase does — the assertions stay in the shared tier, so the npm
and Nix installation paths cannot drift apart in what they guarantee.

`npmInstallHook` prunes dev dependencies out of the build tree before the
check runs, so `preInstall` snapshots `node_modules` with `cp -al` and the
check restores it by copying, leaving the snapshot intact for a replayed
phase.

Two defects fixed in passing, both surfaced by review:

`test:installed` pins a test file by path while the packaging runner sets
`passWithNoTests: true`, so moving that file would have taken the build
green having asserted nothing — the same silently-inert trap `doCheck`
sprang in task 0037. The script now passes `--passWithNoTests=false`.

`checkPhase`'s vitest left a timestamped run cache under
`node_modules/.vite`, which `npmInstallHook` copied into `$out`, shipping
a stray cache and making the derivation non-reproducible. It is now
removed before the install phase; `nix build --rebuild` passes.

CLAUDE.md

@@ -49,6 +49,17 @@ The flip side is the point of the design — touching an ADR, a spec, a task, a
 `buildNpmPackage` provides **no check hook**, so `doCheck = true` on its own is silently inert — the build logs `no Makefile or custom checkPhase, doing nothing` and ships a package whose tests never ran.
 Running the fast tier inside the derivation requires an explicit `checkPhase`; it also needs `git` and `which` in `nativeCheckInputs` and a writable `HOME`, since some of those tests shell out to `git`.
 
+`nodejsInstallExecutables` (inside `npmInstallHook`) installs each manifest `bin` entry as a **generated wrapper that invokes `node <path>` explicitly**, not as a symlink to the entrypoint.
+So under Nix the executable bit on `dist/main.js` is not load-bearing — `chmod -x` on it changes nothing — while the bit on `$out/bin/gitea-axi` is, and makeWrapper always sets it.
+The npm path differs: there the `bin` entry is symlinked and npm sets the bit at install time.
+
+`npmInstallHook` runs `npm prune --omit=dev` against the **build tree's** `node_modules` during `installPhase`, so dev dependencies (vitest included) are gone by the time `postInstall` or `installCheckPhase` runs.
+Anything that needs them after install must snapshot the tree in `preInstall` first; `cp -al` is the cheap way, since the prune's deletions do not follow hardlinks.
+
+Running vitest inside the derivation leaves a run cache at `node_modules/.vite/…/results.json` that records durations and timestamps, and `npmInstallHook` copies `node_modules` into `$out` wholesale.
+Left alone it ships a stray cache in the closure and makes the output non-reproducible — visible only under `nix build --rebuild`, which reports "may not be deterministic"; an ordinary build stays green.
+`checkPhase` deletes it before the install phase runs.
+
 nixpkgs 26.11 (the `nixos-unstable` the flake tracks) has **dropped `x86_64-darwin`**.
 `legacyPackages.x86_64-darwin` now *throws* rather than merely failing to build, so listing that system in the flake's `systems` breaks `nix flake show` and `nix flake check` for every system at once, not just that one.
 Intel macOS would need the 26.05 branch.