feat(nix): expose declarative outputs and a home-manager module (task 0045)

Let a Nix configuration declare gitea-axi's ambient context instead of
running a command that writes it. `setup` and `setup hooks` are write-only
against files the operator is assumed to own, so an operator whose agent
configuration is generated cannot use them at all.

The package installs the bundled Agent Skill to share/gitea-axi/skills and
publishes it as `passthru.skill`, alongside `passthru.sessionStartHook` read
from `session-start-hook.json` — a committed declaration the fast tier reads
too, so a test drives `setup hooks` and asserts the two agree.

On top of that, `homeModules.gitea-axi` declares both from those attributes
through home-manager's own Claude Code options, so an operator's existing
skills and SessionStart hooks compose rather than collide. Importing it
without enabling it yields a byte-identical generation.

The spec's Out of Scope entry deferring a home-manager module is deleted;
ADR 0020 records the reversal, and INSTALL.md describes both paths.

.claude/tasks/0045-declarative-nix-outputs-and-hm-module.md

@@ -32,14 +32,52 @@ The two installation paths remain independent and both supported: the command fo
 
 ## Acceptance criteria
 
-- [ ] The bundled Agent Skill is installed to a stable location in the package output that is not an internal implementation path.
-- [ ] The package exposes the Skill and the hook specification as attributes consumable from a Nix expression without building or running anything.
-- [ ] The hook specification is declared in a single committed file, read by both the Nix expression and the test suite.
-- [ ] A test drives the imperative hook install and asserts that what it writes matches the declared specification, failing if either side drifts.
-- [ ] The flake exposes a home-manager module that declares the Skill and the hook.
-- [ ] Importing the module without enabling it changes nothing about the resulting configuration.
-- [ ] The module installs the package by default, and accepts a null package as the documented way to declare the configuration without installing the binary.
-- [ ] The Skill and the hook each have their own toggle, both defaulting to on.
-- [ ] The module composes with an existing configuration that already declares its own SessionStart hooks and skills, rather than conflicting with it.
-- [ ] The spec's Out of Scope entry excluding a home-manager module is revised, and the decision to reverse it is recorded as an ADR.
-- [ ] The user-facing documentation describes both installation paths and when each applies.
+- [x] The bundled Agent Skill is installed to a stable location in the package output that is not an internal implementation path.
+- [x] The package exposes the Skill and the hook specification as attributes consumable from a Nix expression without building or running anything.
+- [x] The hook specification is declared in a single committed file, read by both the Nix expression and the test suite.
+- [x] A test drives the imperative hook install and asserts that what it writes matches the declared specification, failing if either side drifts.
+- [x] The flake exposes a home-manager module that declares the Skill and the hook.
+- [x] Importing the module without enabling it changes nothing about the resulting configuration.
+- [x] The module installs the package by default, and accepts a null package as the documented way to declare the configuration without installing the binary.
+- [x] The Skill and the hook each have their own toggle, both defaulting to on.
+- [x] The module composes with an existing configuration that already declares its own SessionStart hooks and skills, rather than conflicting with it.
+- [x] The spec's Out of Scope entry excluding a home-manager module is revised, and the decision to reverse it is recorded as an ADR.
+- [x] The user-facing documentation describes both installation paths and when each applies.
+
+## Implementation Notes
+
+The decision is recorded as [ADR 0020](../adr/0020-home-manager-module-for-declarative-context.md).
+The spec's Out of Scope entry is deleted and its "Flake surface" section rewritten to record the reversal rather than to pretend the deferral never happened.
+
+### The hook specification is the settings entry, not its parts
+
+`session-start-hook.json` holds the SessionStart entry verbatim as it belongs in a Claude Code `settings.json` — matcher, and the hook array inside it — rather than the fields the entry is assembled from.
+Declaring the fields would have left the *grouping* restated in both the Nix expression and the test, which is exactly the kind of second source of truth the file exists to prevent.
+As written, the Nix expression is `[ sourcePackage.sessionStartHook ]` and the test is a deep-equality against the same value, so neither restates anything.
+
+The file's contents were derived by observation — running the installed binary against a temporary home and reading what the agent SDK wrote — and the new test was confirmed to fail when the declaration is perturbed, rather than being assumed to bite.
+
+### The module declares through `programs.claude-code`, not through `home.file`
+
+Writing `~/.claude/settings.json` directly would collide with home-manager's own Claude Code module, so the module sets that module's options and lets home-manager's merge semantics compose.
+Verified against real home-manager before landing, on five configurations: importing without enabling produces a **byte-identical** generation to never importing at all; enabling alongside a configuration that already declares its own SessionStart hook and its own skill yields both of each; `package = null` installs no binary but still declares the Skill; the skill-only toggle declares no hook; and omitting `programs.claude-code.enable` fails the assertion with the intended message.
+
+### `package = null` still sources the Skill from the default build
+
+The task called null "the documented opt-out for an operator who supplies the binary another way", which settles where the *binary* comes from but not where the Skill's bytes do.
+They come from the default build, which for the intended case — a system-wide install of this same package — is already in the closure.
+The sharp edge is an operator whose system-wide copy is a different build: their Skill would come from a package they are not running.
+That is documented on the option itself rather than designed away, since the alternative is refusing to declare a Skill at all in the one arrangement the null value exists to serve.
+
+### Two limitations documented rather than fixed
+
+Home-manager inspects the Skill path during evaluation, so a rebuild realises the package at evaluation time even under `package = null`.
+This is inherent to sourcing the Skill from the package and is a rebuild-latency cost, not a correctness one; the alternative would ignore `package` overrides entirely.
+
+`programs.claude-code.skills` also accepts a bare path standing for a whole skills directory, and a configuration using that form cannot have an entry merged into it.
+Both are recorded in INSTALL.md and in the ADR's Consequences.
+
+### Follow-up worth flagging
+
+The repository has no `README.md`, so `INSTALL.md` — which follows the existing convention of topic-scoped root documents alongside `PUBLISHING.md` — is discoverable only by browsing the repository, and is not in the npm `files` allowlist so it does not ship in the tarball.
+Neither was changed here: adding a README is its own piece of work, and installation instructions inside an already-installed tarball are of little use.