chore: use cargo-nextest as the test runner

- .config/nextest.toml: hang-timeout profile (warn 60s, kill 120s)
- justfile: 'just test' = cargo nextest run --workspace + cargo test --doc
- CLAUDE.md: refresh stale Status + Commands for the real workspace + nextest

163 tests run in ~7s (vs multi-minute serial cargo test).

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

justfile

@@ -4,9 +4,11 @@ set dotenv-load
 run:
     cargo run -p server
 
-# Run the full test suite
+# Run the full test suite via cargo-nextest (per-test isolation, live output,
+# hang timeouts). nextest does not run doctests, so they run separately.
 test:
-    cargo test --workspace
+    cargo nextest run --workspace
+    cargo test --workspace --doc
 
 # Format with the nightly toolchain
 fmt: