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.

flake.nix

@@ -40,6 +40,13 @@
       inputs.nixpkgs.follows = "nixpkgs";
     };
 
+    # Agent-ergonomic CLI for Gitea, with its home-manager module wiring in the
+    # Claude Code context where that harness is present.
+    gitea-axi = {
+      url = "git+https://git.alexion.dev/alexion/gitea-axi";
+      inputs.nixpkgs.follows = "nixpkgs";
+    };
+
     # CachyOS kernel and binary cache. Pins its own nixpkgs so its cache stays
     # usable and the kernel is fetched from it.
     chaotic.url = "github:chaotic-cx/nyx/nyxpkgs-unstable";