feat(gitea-axi): install the CLI and wire its agent context

Add gitea-axi as a flake input and a new modules.gitea-axi module that
installs the CLI through its home-manager module. That module also declares
the Claude Code context — the Agent Skill and the SessionStart dashboard hook
— when claude-code is enabled on the host, so neogaia gets both while a host
without the harness would get the CLI alone.

Drop the hand-written SessionStart hook from the claude-code module, which
named a gitea-axi binary nothing installed; the gitea-axi module owns it now.
Remove the vendored skill fork, which had drifted from upstream and would
collide with the copy the module writes.

modules/gitea-axi.nix

@@ -0,0 +1,22 @@
+{
+  config,
+  lib,
+  inputs,
+  ...
+}:
+# gitea-axi for the primary user, installed through its own home-manager module.
+# That module also declares the Claude Code context when that harness is
+# enabled on the host; enabling this alone installs the CLI and nothing else.
+let
+  cfg = config.modules.gitea-axi;
+  user = config.user.name;
+in
+{
+  options.modules.gitea-axi.enable =
+    lib.mkEnableOption "gitea-axi, an agent-ergonomic CLI for Gitea issues and pull requests";
+
+  config = lib.mkIf cfg.enable {
+    home-manager.sharedModules = [ inputs.gitea-axi.homeModules.default ];
+    home-manager.users.${user}.programs.gitea-axi.enable = true;
+  };
+}