change(tooling): typecheck in CI, update ts to 6

fix(ui-tui): fix ts 6 real type errors

change(tooling): use new node everywhere

website/package.json

@@ -14,7 +14,7 @@
     "serve": "docusaurus serve",
     "write-translations": "docusaurus write-translations",
     "write-heading-ids": "docusaurus write-heading-ids",
-    "typecheck": "tsc",
+    "typecheck": "tsc -p . --noEmit",
     "lint:diagrams": "ascii-guard lint --exclude-code-blocks docs"
   },
   "dependencies": {
@@ -32,7 +32,7 @@
     "@docusaurus/module-type-aliases": "3.9.2",
     "@docusaurus/tsconfig": "3.9.2",
     "@docusaurus/types": "3.9.2",
-    "typescript": "~5.6.2"
+    "typescript": "^6.0.3"
   },
   "overrides": {
     "serialize-javascript": "^7.0.5",