Improve live and random live handling

- Add random live handlers, schemas and persistence for lot/play/continue/gameover/reward flow
- Update live status and schedule generation, including special rotation handling and CN timezone alignment
- Add config support for unlocking all daily special rotation songs and document the option
- Refresh live play, reward, precise score and session logic plus bundled main.db updates

Signed-off-by: Sean Du <do4suki@gmail.com>

internal/schema/rlive/util.go

@@ -0,0 +1,7 @@
+package rliveschema
+
+import "strconv"
+
+func itoa(v int) string {
+	return strconv.Itoa(v)
+}