style: apply Prettier formatting to TS/JS/JSON/MD files

Add Prettier as a dev dependency with .prettierrc.json config and
.prettierignore. Hook added via mirrors-prettier in pre-commit config.
All TypeScript, JSON, Markdown, and YAML files auto-formatted.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

package-lock.json

@@ -20,6 +20,7 @@
         "@types/glob": "^8.1.0",
         "@types/node": "^20.19.0",
         "nodemon": "^3.0.1",
+        "prettier": "^3.8.1",
         "typescript": "^5.9.3"
       }
     },
@@ -1150,6 +1151,22 @@
         "node": ">=16.20.0"
       }
     },
+    "node_modules/prettier": {
+      "version": "3.8.1",
+      "resolved": "https://registry.npmjs.org/prettier/-/prettier-3.8.1.tgz",
+      "integrity": "sha512-UOnG6LftzbdaHZcKoPFtOcCKztrQ57WkHDeRD9t/PTQtmT0NHSeWWepj6pS0z/N7+08BHFDQVUrfmfMRcZwbMg==",
+      "dev": true,
+      "license": "MIT",
+      "bin": {
+        "prettier": "bin/prettier.cjs"
+      },
+      "engines": {
+        "node": ">=14"
+      },
+      "funding": {
+        "url": "https://github.com/prettier/prettier?sponsor=1"
+      }
+    },
     "node_modules/proxy-addr": {
       "version": "2.0.7",
       "resolved": "https://registry.npmjs.org/proxy-addr/-/proxy-addr-2.0.7.tgz",