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>

.config/nextest.toml

@@ -0,0 +1,11 @@
+# cargo-nextest configuration. https://nexte.st/book/configuration
+#
+# nextest runs each test in its own process: live per-test output, and a hard
+# per-test timeout so a genuinely wedged test is killed + named rather than
+# stalling the whole run.
+
+[profile.default]
+# Warn at 60s, terminate a test after 2×60s = 120s. The slowest real test is a
+# couple of seconds (each #[sqlx::test] provisions its own temp DB), so this
+# only ever fires on an actual hang.
+slow-timeout = { period = "60s", terminate-after = 2 }