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/lot.go

@@ -0,0 +1,36 @@
+package rliveschema
+
+import liveschema "honoka-chan/internal/schema/live"
+
+type LotReq struct {
+	Module         string `json:"module"`
+	Action         string `json:"action"`
+	MemberCategory int    `json:"member_category"`
+	Mgd            int    `json:"mgd"`
+	Difficulty     int    `json:"difficulty"`
+	Attribute      int    `json:"attribute"`
+	TimeStamp      int64  `json:"timeStamp"`
+	CommandNum     string `json:"commandNum"`
+}
+
+type LiveInfo struct {
+	LiveDifficultyID int  `json:"live_difficulty_id"`
+	IsRandom         bool `json:"is_random"`
+	AcFlag           int  `json:"ac_flag"`
+	SwingFlag        int  `json:"swing_flag"`
+}
+
+type LotData struct {
+	LiveInfo          LiveInfo               `json:"live_info"`
+	HasSlideNotes     int                    `json:"has_slide_notes"`
+	PartyList         []liveschema.PartyList `json:"party_list"`
+	TrainingEnergy    int                    `json:"training_energy"`
+	TrainingEnergyMax int                    `json:"training_energy_max"`
+	Token             string                 `json:"token"`
+}
+
+type LotResp struct {
+	ResponseData LotData `json:"response_data"`
+	ReleaseInfo  []any   `json:"release_info"`
+	StatusCode   int     `json:"status_code"`
+}