chore(config): gate cargo test in pre-push on Rust changes

Add `cargo test --quiet` to the pre-push Rust block (sharing clippy's
target/ guard) so the suite runs automatically on every push touching
server/. Nothing ran the tests before — pre-push did only fmt/clippy/deny
and there is no CI — so a Rust regression could reach main unverified.

Document the resulting agent-spawn rule in team-patterns.md: don't have
implementation agents pre-run fmt/clippy/test pre-emptively, since the push
gate now enforces all three. The gate is authoritative; the lead patches any
fallout at push.

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

.config/hooks/pre-push

@@ -97,8 +97,19 @@ elif command -v cargo >/dev/null 2>&1 && [ -d "$REPO_ROOT/server" ]; then
         else
             echo "pre-push: clippy — OK"
         fi
+
+        # cargo test — the ONLY automatic correctness gate: nothing else (no CI
+        # workflows exist) runs the suite, so without this a Rust regression
+        # reaches main unverified. Gated on server/ changes; shares the target/
+        # guard with clippy so a cold worktree isn't forced into a full build.
+        echo "pre-push: checking Rust (cargo test)..."
+        if ! (cd "$REPO_ROOT/server" && cargo test --quiet 2>&1); then
+            ERRORS=$((ERRORS + 1))
+        else
+            echo "pre-push: cargo test — OK"
+        fi
     else
-        echo "pre-push: skipping clippy (no target/ — run 'cargo build' once to enable)"
+        echo "pre-push: skipping clippy + test (no target/ — run 'cargo build' once to enable)"
     fi
 
     # --- Rust dependency audit (cargo deny) — requires deny.toml config ---