Can AI replace Grammarly?

Build me a personal writing checker to replace Grammarly. Requirements:

- Grammar engine: LanguageTool running locally via its official Docker image;
  grammar checks never leave my machine.
- A local web page (Node + Express, binds to localhost): paste text, see
  LanguageTool issues underlined with hover explanations, click a suggestion
  to apply it.
- An LLM rewrite pane (key in .env) with three buttons: tighten, friendlier,
  formal. Show a diff against my original before I accept anything.
- A personal dictionary file (dictionary.txt) of names and jargon to never
  flag, passed to LanguageTool on every check.
- CLI mode: `check <file.md>` prints issues with line numbers, exits nonzero
  if any, so it can run as a git pre-commit hook on docs.
- Everything local except the optional LLM call; no accounts, no telemetry.
- Out of scope: a browser extension and inline suggestions inside Gmail,
  Docs, or Slack. This is a destination I paste into, that is the honest
  trade against Grammarly.
- README: Docker setup for LanguageTool, the roughly 1 GB of RAM it wants,
  and where the LLM key goes.