Refactor provider dispatch behind a Backend trait

[bddap-bot]

PR A of the two-PR plan in #31: a pure refactor that introduces a common provider interface, no behavior change. PR B (function-call edits, the #31 rewrite) stacks on this.

What

main.rs::refactor() matched on Provider, re-derived the API key inline, and called a free anthropic::complete / openai::complete. That match-and-duplicate is exactly what gets ugly when a second call shape (tool edits) lands.

• New src/backend.rs: trait Backend { fn complete(&self, &[Message]) -> Result<String>; } and resolve(provider, model, &secrets) -> Result<Box<dyn Backend>> — the one place that knows how each provider sources its key and errors when it's missing.
• anthropic.rs / openai.rs each gain an Anthropic / Openai struct that impl Backend, forwarding to the (now private) send() wire call.
• refactor() collapses to backend::resolve(provider, &model, sc)?.complete(&messages).

Why Box<dyn Backend> and not a closed enum

Tool/function-call edits (PR B) are Anthropic-only. A trait expresses that as a separate Edits trait that only Anthropic implements — no enum arm faking "unsupported" at runtime. Documented in backend.rs.

No behavior change

Wire formats untouched. The "no key" trigger conditions and messages are byte-identical (moved verbatim into resolve). Provider/model resolution unchanged.

Tests

cargo test → 7 passing (the 5 existing + 2 new resolve tests covering missing-key and present-key for both providers). clippy clean on the changed files. Built with nixpkgs rust 1.91.

Self-reviewed via two rounds of fan-out review agents (correctness, security, Niko-style design): no correctness/security findings; applied the design refinements (borrow model, rename the private wire fn to send, document the dyn choice).

🤖 Generated with Claude Code

[bddap-bot]

Obsoleted by #33. #33 cuts the whole-text rewrite path entirely (owner's call — personal tool, no need to keep it), so the Backend-trait refactor this PR introduced for the rewrite dispatch is moot. The edit-mode work lives in #33, which now stands alone.