build(layer1): isolate Next output to .build/next; gitignore .build/ dist/ .next/

- next.config.mjs: distDir default ".next" → ".build/next" (NEXT_DIST_DIR override kept)
- .gitignore: add /.build/, /dist/, /.next/; remove loose dist/ under #dependencies
- scripts/build/paths.mjs: new shared module exporting ROOT, DIST_DIR, STANDALONE_DIR
- scripts/build/build-next-isolated.mjs: default ".next" → ".build/next" in distDir,
  resetStandaloneOutput fallback, and pruneStandaloneArtifacts
- scripts/build/prepublish.ts: NEXT_DIST default ".next" → ".build/next"
- scripts/build/assembleStandalone.mjs: legacy syncStandalone* helpers updated
  to resolve distDir via NEXT_DIST_DIR || ".build/next"
- tsconfig.json: Next.js auto-added .build/next/types includes (generated on build)

Smoke: .build/next/standalone/server.js exists; BUNDLE_OK confirmed;
no .next directory created.

tsconfig.json

@@ -1,7 +1,11 @@
 {
   "compilerOptions": {
     "target": "ES2022",
-    "lib": ["dom", "dom.iterable", "esnext"],
+    "lib": [
+      "dom",
+      "dom.iterable",
+      "esnext"
+    ],
     "allowJs": true,
     "checkJs": false,
     "skipLibCheck": true,
@@ -17,9 +21,15 @@
     "incremental": true,
     "forceConsistentCasingInFileNames": true,
     "paths": {
-      "@/*": ["./src/*"],
-      "@omniroute/open-sse": ["./open-sse"],
-      "@omniroute/open-sse/*": ["./open-sse/*"]
+      "@/*": [
+        "./src/*"
+      ],
+      "@omniroute/open-sse": [
+        "./open-sse"
+      ],
+      "@omniroute/open-sse/*": [
+        "./open-sse/*"
+      ]
     },
     "plugins": [
       {
@@ -37,7 +47,9 @@
     ".next/dev/types/**/*.ts",
     ".next/dev/dev/types/**/*.ts",
     ".next-playwright/types/**/*.ts",
-    ".next-playwright/dev/types/**/*.ts"
+    ".next-playwright/dev/types/**/*.ts",
+    ".build/next/types/**/*.ts",
+    ".build/next/dev/types/**/*.ts"
   ],
   "exclude": [
     "node_modules",