feat: integrate DB with Open/Close/Put/Delete/Get

- Add db.go with DB struct: Open/Close/Put/Delete/Get/GetDurableSequence/IsWriteStopped
- Add db_test.go with lifecycle, put/get, delete, recovery, and corruption tests
- Extract sentinel errors to errkit/ leaf package to break import cycle (wal -> go_kv)
- Update wal/sequence.go, wal/writer.go to import errkit instead of root package
- Root errors.go re-exports from errkit for backward compatibility

Phase 1 Wave 4d complete (T19).

db_test.go

@@ -0,0 +1,176 @@
+package go_kv
+
+import (
+	"fmt"
+	"os"
+	"path/filepath"
+	"testing"
+)
+
+func TestDBOpenClose(t *testing.T) {
+	db, err := Open(t.TempDir(), nil)
+	if err != nil {
+		t.Fatalf("Open: %v", err)
+	}
+	if err := db.Put([]byte("k"), []byte("v")); err != nil {
+		t.Fatalf("Put: %v", err)
+	}
+	if err := db.Close(); err != nil {
+		t.Fatalf("Close: %v", err)
+	}
+}
+
+func TestDBPutGet(t *testing.T) {
+	db := openTestDB(t, t.TempDir())
+
+	if err := db.Put([]byte("k1"), []byte("v1")); err != nil {
+		t.Fatalf("Put: %v", err)
+	}
+
+	got := db.Get([]byte("k1"))
+	if !got.Found {
+		t.Fatal("Get(k1) not found")
+	}
+	if string(got.Value) != "v1" {
+		t.Fatalf("Get(k1) value = %q, want %q", got.Value, "v1")
+	}
+}
+
+func TestDBDelete(t *testing.T) {
+	db := openTestDB(t, t.TempDir())
+
+	if err := db.Put([]byte("k"), []byte("v")); err != nil {
+		t.Fatalf("Put: %v", err)
+	}
+	if err := db.Delete([]byte("k")); err != nil {
+		t.Fatalf("Delete: %v", err)
+	}
+
+	got := db.Get([]byte("k"))
+	if got.Found {
+		t.Fatalf("Get(k) found deleted key with value %q", got.Value)
+	}
+}
+
+func TestDBRecovery(t *testing.T) {
+	dir := t.TempDir()
+	db := openTestDB(t, dir)
+
+	entries := map[string]string{
+		"k1": "v1",
+		"k2": "v2",
+		"k3": "v3",
+	}
+	for key, value := range entries {
+		if err := db.Put([]byte(key), []byte(value)); err != nil {
+			t.Fatalf("Put(%q): %v", key, err)
+		}
+	}
+	closeTestDB(t, db)
+
+	reopened := openTestDB(t, dir)
+	for key, want := range entries {
+		got := reopened.Get([]byte(key))
+		if !got.Found {
+			t.Fatalf("Get(%q) not found after recovery", key)
+		}
+		if string(got.Value) != want {
+			t.Fatalf("Get(%q) value = %q, want %q", key, got.Value, want)
+		}
+	}
+}
+
+func TestDBRecoveryAfterCorruption(t *testing.T) {
+	dir := t.TempDir()
+	db := openTestDB(t, dir)
+
+	if err := db.Put([]byte("good1"), []byte("v1")); err != nil {
+		t.Fatalf("Put good1: %v", err)
+	}
+	if err := db.Put([]byte("good2"), []byte("v2")); err != nil {
+		t.Fatalf("Put good2: %v", err)
+	}
+	closeTestDB(t, db)
+
+	appendWalTail(t, dir, []byte{0xde, 0xad, 0xbe, 0xef})
+
+	reopened := openTestDB(t, dir)
+	for key, want := range map[string]string{"good1": "v1", "good2": "v2"} {
+		got := reopened.Get([]byte(key))
+		if !got.Found {
+			t.Fatalf("Get(%q) not found after corrupted-tail recovery", key)
+		}
+		if string(got.Value) != want {
+			t.Fatalf("Get(%q) value = %q, want %q", key, got.Value, want)
+		}
+	}
+}
+
+func TestDBMultiplePuts(t *testing.T) {
+	dir := t.TempDir()
+	db := openTestDB(t, dir)
+
+	for i := range 50 {
+		key := fmt.Appendf(nil, "k%d", i)
+		value := fmt.Appendf(nil, "v%d", i)
+		if err := db.Put(key, value); err != nil {
+			t.Fatalf("Put(%q): %v", key, err)
+		}
+	}
+	closeTestDB(t, db)
+
+	reopened := openTestDB(t, dir)
+	for i := range 50 {
+		key := fmt.Appendf(nil, "k%d", i)
+		want := fmt.Sprintf("v%d", i)
+		got := reopened.Get(key)
+		if !got.Found {
+			t.Fatalf("Get(%q) not found after recovery", key)
+		}
+		if string(got.Value) != want {
+			t.Fatalf("Get(%q) value = %q, want %q", key, got.Value, want)
+		}
+	}
+}
+
+func openTestDB(t *testing.T, dir string) *DB {
+	t.Helper()
+
+	db, err := Open(dir, nil)
+	if err != nil {
+		t.Fatalf("Open: %v", err)
+	}
+	t.Cleanup(func() {
+		if !db.closed.Load() {
+			if err := db.Close(); err != nil {
+				t.Fatalf("Close cleanup: %v", err)
+			}
+		}
+	})
+	return db
+}
+
+func closeTestDB(t *testing.T, db *DB) {
+	t.Helper()
+	if err := db.Close(); err != nil {
+		t.Fatalf("Close: %v", err)
+	}
+}
+
+func appendWalTail(t *testing.T, dir string, tail []byte) {
+	t.Helper()
+
+	path := filepath.Join(dir, "segment-0.wal")
+	f, err := os.OpenFile(path, os.O_APPEND|os.O_WRONLY, 0)
+	if err != nil {
+		t.Fatalf("OpenFile(%s): %v", path, err)
+	}
+	defer func() {
+		if err := f.Close(); err != nil {
+			t.Fatalf("Close corrupted WAL file: %v", err)
+		}
+	}()
+	if _, err := f.Write(tail); err != nil {
+		t.Fatalf("Write corrupted WAL tail: %v", err)
+	}
+}