refactor(backend): extract pagination utilities

Issue #4: Pagination logic was repeated across multiple routes.

Changes:
- Add pagination.py with reusable utilities:
  - calculate_total_pages: computes page count from total/per_page
  - calculate_offset: computes offset for given page
  - create_paginated_response: builds PaginatedResponse with metadata
- Update routes/audit.py to use pagination utilities
- Update routes/booking.py to use pagination utilities
- Update routes/invites.py to use pagination utilities

The utilities handle the common pagination math while routes
still manage their own query logic (filters, joins, ordering).

backend/routes/audit.py

@@ -11,6 +11,11 @@ from sqlalchemy.ext.asyncio import AsyncSession
 from auth import require_permission
 from database import get_db
 from models import CounterRecord, Permission, RandomNumberOutcome, SumRecord, User
+from pagination import (
+    calculate_offset,
+    calculate_total_pages,
+    create_paginated_response,
+)
 from schemas import (
     CounterRecordResponse,
     PaginatedCounterRecords,
@@ -39,10 +44,9 @@ async def paginate_with_user_email(
     # Get total count
     count_result = await db.execute(select(func.count(model.id)))
     total = count_result.scalar() or 0
-    total_pages = (total + per_page - 1) // per_page if total > 0 else 1
 
     # Get paginated records with user email
-    offset = (page - 1) * per_page
+    offset = calculate_offset(page, per_page)
     query = (
         select(model, User.email)
         .join(User, model.user_id == User.id)
@@ -54,7 +58,7 @@ async def paginate_with_user_email(
     rows = result.all()
 
     records: list[R] = [row_mapper(record, email) for record, email in rows]
-    return records, total, total_pages
+    return records, total, calculate_total_pages(total, per_page)
 
 
 def _map_counter_record(record: CounterRecord, email: str) -> CounterRecordResponse:
@@ -86,16 +90,10 @@ async def get_counter_records(
     _current_user: User = Depends(require_permission(Permission.VIEW_AUDIT)),
 ) -> PaginatedCounterRecords:
     """Get paginated counter action records."""
-    records, total, total_pages = await paginate_with_user_email(
+    records, total, _ = await paginate_with_user_email(
         db, CounterRecord, page, per_page, _map_counter_record
     )
-    return PaginatedCounterRecords(
-        records=records,
-        total=total,
-        page=page,
-        per_page=per_page,
-        total_pages=total_pages,
-    )
+    return create_paginated_response(records, total, page, per_page)
 
 
 @router.get("/sum", response_model=PaginatedSumRecords)
@@ -106,16 +104,10 @@ async def get_sum_records(
     _current_user: User = Depends(require_permission(Permission.VIEW_AUDIT)),
 ) -> PaginatedSumRecords:
     """Get paginated sum action records."""
-    records, total, total_pages = await paginate_with_user_email(
+    records, total, _ = await paginate_with_user_email(
         db, SumRecord, page, per_page, _map_sum_record
     )
-    return PaginatedSumRecords(
-        records=records,
-        total=total,
-        page=page,
-        per_page=per_page,
-        total_pages=total_pages,
-    )
+    return create_paginated_response(records, total, page, per_page)
 
 
 @router.get("/random-jobs", response_model=list[RandomNumberOutcomeResponse])