feat(pi): install the coding agent for a side-by-side trial (task 0020)

Add a `pi` module that turns on the home-manager `programs.pi-coding-agent`
integration for the primary user and freezes a single settings.json: the
default provider set to Anthropic, the default model to Opus (claude-opus-4-8,
Pi's own catalogue id), and analytics disabled. Everything else in
~/.pi/agent — the credential and all self-modification state — is left
unmanaged, so login survives rebuilds and backing Pi out is a one-line enable
flip. Enabled on neogaia alone.

modules/pi/pi.nix

@@ -0,0 +1,37 @@
+{
+  config,
+  lib,
+  ...
+}:
+# Pi, a terminal coding agent, for the primary user, configured through
+# home-manager, which ships the package and manages ~/.pi/agent.
+# The login credential is left unmanaged, so it survives rebuilds.
+let
+  cfg = config.modules.pi;
+  user = config.user.name;
+in
+{
+  options.modules.pi.enable = lib.mkEnableOption ''
+    Pi, a terminal coding agent, configured via home-manager.
+
+    Pins the provider to Anthropic and the model to Opus so Pi runs the same
+    model as Claude Code, and disables analytics. Authentication reuses an
+    existing Claude subscription and is deliberately left unmanaged, so no
+    credential enters the repo and re-auth survives rebuilds'';
+
+  config = lib.mkIf cfg.enable {
+    home-manager.users.${user}.programs.pi-coding-agent = {
+      enable = true;
+
+      # settings.json is the only file here Pi writes at runtime, and only its
+      # analytics keys. Disabling analytics removes that write, so freezing the
+      # file never fights Pi's self-modification, which targets other paths.
+      settings = {
+        defaultProvider = "anthropic";
+        # Pi's catalogue id for Opus.
+        defaultModel = "claude-opus-4-8";
+        enableAnalytics = false;
+      };
+    };
+  };
+}