style(backend): rustfmt the whole tree; gate cargo fmt --check in CI

The backend had never been run through rustfmt. Doing it in one mechanical pass (134 files)
so no future functional diff is buried under formatting churn, then gating `cargo fmt
--check` in checks.yml so it stays clean.

Formatting only — no logic, SQL, or behaviour changed. Verified after the reformat:
cargo test 56 passed, clippy --all-targets -D warnings clean, cargo fmt --check clean.

This is the deferred cleanup noted when CI's Format step was first left out.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

.github/workflows/checks.yml

@@ -66,9 +66,9 @@ jobs:
         working-directory: ./backend
         run: cargo clippy --all-targets -- -D warnings
 
-      # NOTE: `cargo fmt --check` is deliberately NOT gated. The tree has never been rustfmt'd, so
-      # turning it on means a 112-file mechanical reformat that would bury every real diff under it.
-      # Formatting is not a correctness gate; do that cleanup on its own, then add the check here.
+      - name: Format
+        working-directory: ./backend
+        run: cargo fmt --check
 
   frontend:
     name: Frontend — vitest + svelte-check