feat(mail): DB 저장 + 주기 동기화 + 전체 히스토리 수집 + 메일 숨김

- ProjectMailMsg(헤더 저장)·ProjectMailState(동기화 상태) 모델, AutoMigrate 등록
- mailsync.FetchForDomain: nextPageToken 따라 전체 히스토리 페이지네이션(maxPerBox=0=전부)
- 백그라운드 주기 동기화 StartMailSyncLoop(MAIL_SYNC_INTERVAL 기본 15m, 0=비활성)
  · 미동기화 프로젝트=full 백필, 이후=최신 페이지 top-up
- GET /mails는 DB에서 읽어 참여자(from/to/cc) 필터 + 공동 메모 인라인 결합 + lastSyncedAt
- POST /mails/sync(강제 풀싱크), PUT /mail-hide(프로젝트 단위 숨김)
- mailCache 제거(DB가 캐시), config MailSyncInterval

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

internal/models/models.go

@@ -28,7 +28,8 @@ func All() []interface{} {
 		&Attendance{}, &LeaveRequest{}, &OvertimeRequest{}, &WorkPolicy{}, &LeaveBalance{},
 		// slice 3 — projects
 		&Company{}, &Product{}, &Version{}, &Project{}, &ProjectMember{},
-		&ClientContact{}, &ProjectTask{}, &TaskComment{}, &MailNote{}, &Contract{}, &ContractFile{}, &PaymentSplit{},
+		&ClientContact{}, &ProjectTask{}, &TaskComment{}, &MailNote{}, &ProjectMailMsg{}, &ProjectMailState{},
+		&Contract{}, &ContractFile{}, &PaymentSplit{},
 		// slice 4 — incentive
 		&IncentiveConfig{}, &PaymentStage{}, &UserIncentive{}, &QuarterlySettlement{},
 		// slice 5 — accounting

internal/models/project.go

@@ -140,6 +140,37 @@ type MailNote struct {
 
 func (m *MailNote) BeforeCreate(*gorm.DB) error { m.ensureID(); return nil }
 
+// ProjectMailMsg is a stored mail header for a project's client domain (본문 미저장,
+// 헤더/스니펫만). 동기화 시 (project, Message-ID)로 upsert. Hidden=프로젝트에서 숨김.
+type ProjectMailMsg struct {
+	Base
+	ProjectID string    `gorm:"index:idx_pmm,unique" json:"projectId"`
+	MessageID string    `gorm:"index:idx_pmm,unique" json:"messageId"`
+	ThreadID  string    `json:"threadId"`
+	FromAddr  string    `json:"from"`
+	ToAddr    string    `json:"to"`
+	CcAddr    string    `json:"cc"`
+	Subject   string    `json:"subject"`
+	Snippet   string    `json:"snippet"`
+	DateHdr   string    `json:"date"`
+	Mailbox   string    `json:"mailbox"`
+	TS        int64     `gorm:"index" json:"ts"`
+	Hidden    bool      `json:"hidden"`
+	HiddenBy  string    `json:"hiddenBy"`
+	CreatedAt time.Time `json:"createdAt"`
+	UpdatedAt time.Time `json:"updatedAt"`
+}
+
+func (m *ProjectMailMsg) BeforeCreate(*gorm.DB) error { m.ensureID(); return nil }
+
+// ProjectMailState tracks the last mail sync per project.
+type ProjectMailState struct {
+	ProjectID    string     `gorm:"primaryKey" json:"projectId"`
+	LastSyncedAt *time.Time `json:"lastSyncedAt"`
+	LastError    string     `json:"lastError"`
+	Count        int        `json:"count"`
+}
+
 // Contract holds the [admin-only] commercial terms of a project. BE is the
 // break-even floor (손해가 안 나는 최소 금액). Exposed ONLY to admins.
 type Contract struct {