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/handler/live/continue.go

@@ -14,7 +14,11 @@ func continuee(ctx *gin.Context) {
 	ss := session.Get(ctx)
 	defer ss.Finalize()
 
-	ss.Respond(liveschema.ContinueResp{
+	ss.Respond(BuildContinueResp(ss))
+}
+
+func BuildContinueResp(ss *session.Session) liveschema.ContinueResp {
+	return liveschema.ContinueResp{
 		ResponseData: liveschema.ContinueData{
 			BeforeSnsCoin:   ss.UserPref.SnsCoin,
 			AfterSnsCoin:    ss.UserPref.SnsCoin,
@@ -22,7 +26,7 @@ func continuee(ctx *gin.Context) {
 		},
 		ReleaseInfo: []any{},
 		StatusCode:  200,
-	})
+	}
 }
 
 func init() {