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/mailsync/mailsync.go

@@ -112,9 +112,10 @@ func New(credsPath string) *Service {
 // Enabled reports whether real Gmail access is configured.
 func (s *Service) Enabled() bool { return s != nil && s.sa != nil }
 
-// ListForDomain impersonates each mailbox in turn, searches it for the client
-// domain, and returns the aggregated, de-duplicated, newest-first list (<= max).
-func (s *Service) ListForDomain(ctx context.Context, mailboxes []string, domain string, max int) ([]Message, error) {
+// FetchForDomain impersonates each mailbox in turn and pages through its full
+// history for the client domain (maxPerBox caps pages per mailbox; <=0 = all),
+// returning the aggregated, de-duplicated, newest-first list.
+func (s *Service) FetchForDomain(ctx context.Context, mailboxes []string, domain string, maxPerBox int) ([]Message, error) {
 	if !s.Enabled() {
 		return nil, nil
 	}
@@ -122,7 +123,9 @@ func (s *Service) ListForDomain(ctx context.Context, mailboxes []string, domain
 	if domain == "" {
 		return nil, nil
 	}
-	perBox := 25
+	if maxPerBox <= 0 {
+		maxPerBox = 1 << 30 // effectively unbounded (whole history)
+	}
 	q := fmt.Sprintf("(from:%s OR to:%s OR cc:%s) -in:chats", domain, domain, domain)
 	seen := map[string]bool{}
 	var all []Message
@@ -132,65 +135,77 @@ func (s *Service) ListForDomain(ctx context.Context, mailboxes []string, domain
 		if box == "" {
 			continue
 		}
-		ids, err := s.listIDs(ctx, box, q, perBox)
-		if err != nil {
-			if firstErr == nil {
-				firstErr = err
-			}
-			continue
-		}
-		for _, id := range ids {
-			m, err := s.getMeta(ctx, box, id)
+		pageToken := ""
+		fetched := 0
+		for {
+			ids, next, err := s.listPage(ctx, box, q, pageToken)
 			if err != nil {
-				continue
+				if firstErr == nil {
+					firstErr = err
+				}
+				break
 			}
-			key := m.ID
-			if key == "" {
-				key = box + "/" + id
+			for _, id := range ids {
+				if fetched >= maxPerBox {
+					break
+				}
+				m, err := s.getMeta(ctx, box, id)
+				if err != nil {
+					continue
+				}
+				key := m.ID
+				if key == "" {
+					key = box + "/" + id
+				}
+				if !seen[key] {
+					seen[key] = true
+					all = append(all, m)
+				}
+				fetched++
 			}
-			if seen[key] {
-				continue
+			if next == "" || fetched >= maxPerBox {
+				break
 			}
-			seen[key] = true
-			all = append(all, m)
+			pageToken = next
 		}
 	}
 	sort.Slice(all, func(i, j int) bool { return all[i].TS > all[j].TS })
-	if max > 0 && len(all) > max {
-		all = all[:max]
-	}
 	return all, firstErr
 }
 
-func (s *Service) listIDs(ctx context.Context, subject, q string, max int) ([]string, error) {
+func (s *Service) listPage(ctx context.Context, subject, q, pageToken string) (ids []string, next string, err error) {
 	tok, err := s.accessToken(ctx, subject)
 	if err != nil {
-		return nil, err
+		return nil, "", err
+	}
+	u := fmt.Sprintf("https://gmail.googleapis.com/gmail/v1/users/me/messages?maxResults=100&q=%s", url.QueryEscape(q))
+	if pageToken != "" {
+		u += "&pageToken=" + url.QueryEscape(pageToken)
 	}
-	u := fmt.Sprintf("https://gmail.googleapis.com/gmail/v1/users/me/messages?maxResults=%d&q=%s", max, url.QueryEscape(q))
 	req, _ := http.NewRequestWithContext(ctx, http.MethodGet, u, nil)
 	req.Header.Set("Authorization", "Bearer "+tok)
 	resp, err := s.client.Do(req)
 	if err != nil {
-		return nil, err
+		return nil, "", err
 	}
 	defer resp.Body.Close()
 	if resp.StatusCode >= 300 {
-		return nil, fmt.Errorf("gmail list %d for %s", resp.StatusCode, subject)
+		return nil, "", fmt.Errorf("gmail list %d for %s", resp.StatusCode, subject)
 	}
 	var out struct {
 		Messages []struct {
 			ID string `json:"id"`
 		} `json:"messages"`
+		NextPageToken string `json:"nextPageToken"`
 	}
 	if err := json.NewDecoder(resp.Body).Decode(&out); err != nil {
-		return nil, err
+		return nil, "", err
 	}
-	ids := make([]string, 0, len(out.Messages))
+	ids = make([]string, 0, len(out.Messages))
 	for _, m := range out.Messages {
 		ids = append(ids, m.ID)
 	}
-	return ids, nil
+	return ids, out.NextPageToken, nil
 }
 
 func (s *Service) getMeta(ctx context.Context, subject, id string) (Message, error) {