Can AI replace Claude?

Build me a personal chat client on the Anthropic API to replace my Claude Pro
subscription with per-token billing. Requirements:

- A local web app: Node + Express + better-sqlite3, streaming replies over SSE,
  a conversation sidebar, Markdown rendering with marked.
- Anthropic API key in .env; model picker with Sonnet as the default and Opus
  on demand; system prompt editable and saved per project.
- Projects: a project groups conversations and holds a few reference docs
  (plain text or PDF via pdf-parse) prepended as context for every chat inside
  it.
- Use prompt caching on the project docs to cut token costs, the API supports
  it directly.
- SQLite FTS5 search across all conversations; export any thread to Markdown.
- A cost meter per conversation plus a monthly total from the API usage fields,
  so the keep-paying-or-not decision is a number, not a feeling.
- Localhost only, no accounts, no telemetry.
- Out of scope: artifacts, mobile apps, and agent features. If the cost meter
  shows heavy use, flat-rate Pro or Max wins; include that comparison logic in
  the README.
- README: key setup, a link to current per-token prices, and state that the
  model is the product; this wrapper only changes how I pay for it.