feat(nix): package gitea-axi as a flake with a PATH-suffixing wrapper (task 0037)

Add a flake at the repository root exposing gitea-axi as a package, with the
derivation in its own callable expression so it stays buildable outside a flake
context and usable in an overlay unchanged.

Dependencies are fetched from the lockfile's integrity fields via importNpmLock
rather than a committed fixed-output hash, and the version is read from the
package manifest, so neither a dependency bump nor a release edits any Nix
expression. The source is an explicit allowlist, keeping ADR, spec, task and
bench churn out of the derivation's inputs.

The installed binary is wrapped with --suffix PATH per ADR 0018: the operator's
own git and tea win, and the closure's are a fresh-machine fallback.

Two things differ from the plan. Systems coverage is three targets, not four:
nixpkgs 26.11 dropped x86_64-darwin and now throws on evaluating it, which
would break nix flake show and nix flake check for every system at once. And
buildNpmPackage supplies no check hook, so doCheck alone was silently inert and
produced a green build whose tests never ran; running the fast tier needs an
explicit checkPhase.

.claude/tasks/0042-verify-hook-path-resolution.md

@@ -23,3 +23,27 @@ Changing the `setup` command to prefer the bare name is explicitly **not** part
 - [ ] The finding is recorded where a future reader will meet it, so the question is not re-opened from scratch.
 - [ ] If the absolute path is recorded, the documentation states that hook setup must be re-run after an upgrade.
 - [ ] No change is made to how the `setup` command constructs the hook in this task.
+
+## Evidence gathered during task 0037
+
+Task 0037 built the flake, which made the SDK's behaviour directly observable.
+The answer is the unfavourable one: **the absolute path is recorded**, so the mitigation branch of this task applies, not the close-the-item branch.
+
+`resolvePortableHookCommand` in `axi-sdk-js` returns the bare binary name only when a `PATH` entry realpath-matches the entrypoint, and the absolute path in every other case.
+Driving the Nix-built binary writes this into `~/.claude/settings.json`:
+
+```
+/nix/store/nmkzjny0hpzjvyxzdz189whk605di8b6-gitea-axi-0.1.0/lib/node_modules/gitea-axi/dist/main.js
+```
+
+That path is content-addressed, so it changes on every rebuild and is eventually garbage-collected, and the session-start hook then silently stops running.
+
+A second defect surfaced from the same line.
+`isManagedHook` recognises its own hook by testing whether the recorded command *string contains* the marker `"gitea-axi"`, so when the entrypoint path lacks that substring, `setup hooks` appends a duplicate entry instead of updating in place — contradicting the idempotency its help text promises.
+This is reproducible outside Nix: copy the checkout to a path containing no `gitea-axi` segment and `test/setup.test.ts` fails.
+
+Consequences for this task:
+
+- Both defects trace to the same resolution line, so they should be weighed together.
+- The stale store path is user-facing breakage on the install method task 0037 added, which argues for not letting this drift far behind it.
+- `package.nix` carries a `postUnpack` rename of the build tree purely to work around the substring coupling. It is commented as a workaround and should be **deleted as part of this task**, once the hook no longer depends on the entrypoint path.