refactor(backend): strengthen domain layer types and add missing page types

- DomainError struct with Code() string method replaces plain errors.New
  sentinels; errors.Is() still works via pointer equality
- UUIDCreatedAt(uuid.UUID) time.Time helper extracts timestamp from UUID v7
- Add TagOffsetPage, CategoryOffsetPage, PoolOffsetPage
- FileListParams fields grouped with comments matching openapi.yaml params
- Fix mismatched comment on UserPage

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/internal/domain/category.go

@@ -17,5 +17,13 @@ type Category struct {
 	CreatorID   int16
 	CreatorName string // denormalized
 	IsPublic    bool
-	CreatedAt   time.Time // extracted from UUID v7
+	CreatedAt   time.Time // extracted from UUID v7 via UUIDCreatedAt
+}
+
+// CategoryOffsetPage is an offset-based page of categories.
+type CategoryOffsetPage struct {
+	Items  []Category
+	Total  int
+	Offset int
+	Limit  int
 }

backend/internal/domain/errors.go

@@ -1,13 +1,21 @@
 package domain
 
-import "errors"
+// DomainError is a typed domain error with a stable machine-readable code.
+// Handlers map these codes to HTTP status codes.
+type DomainError struct {
+	code    string
+	message string
+}
 
-// Sentinel domain errors. Handlers map these to HTTP status codes.
+func (e *DomainError) Error() string { return e.message }
+func (e *DomainError) Code() string  { return e.code }
+
+// Sentinel domain errors. Use errors.Is(err, domain.ErrNotFound) for matching.
 var (
-	ErrNotFound        = errors.New("not found")
-	ErrForbidden       = errors.New("forbidden")
-	ErrUnauthorized    = errors.New("unauthorized")
-	ErrConflict        = errors.New("conflict")
-	ErrValidation      = errors.New("validation error")
-	ErrUnsupportedMIME = errors.New("unsupported MIME type")
+	ErrNotFound        = &DomainError{"not_found", "not found"}
+	ErrForbidden       = &DomainError{"forbidden", "forbidden"}
+	ErrUnauthorized    = &DomainError{"unauthorized", "unauthorized"}
+	ErrConflict        = &DomainError{"conflict", "conflict"}
+	ErrValidation      = &DomainError{"validation_error", "validation error"}
+	ErrUnsupportedMIME = &DomainError{"unsupported_mime", "unsupported MIME type"}
 )

backend/internal/domain/file.go

@@ -29,21 +29,26 @@ type File struct {
 	CreatorName     string // denormalized from core.users
 	IsPublic        bool
 	IsDeleted       bool
-	CreatedAt       time.Time // extracted from UUID v7
+	CreatedAt       time.Time // extracted from UUID v7 via UUIDCreatedAt
 	Tags            []Tag     // loaded with the file
 }
 
 // FileListParams holds all parameters for listing/filtering files.
 type FileListParams struct {
-	Filter    string
-	Sort      string
-	Order     string
+	// Pagination
 	Cursor    string
-	Anchor    *uuid.UUID
 	Direction string // "forward" or "backward"
+	Anchor    *uuid.UUID
 	Limit     int
-	Trash     bool
-	Search    string
+
+	// Sorting
+	Sort  string // "content_datetime" | "created" | "original_name" | "mime"
+	Order string // "asc" | "desc"
+
+	// Filtering
+	Filter string // filter DSL expression
+	Search string // substring match on original_name
+	Trash  bool   // if true, return only soft-deleted files
 }
 
 // FilePage is the result of a cursor-based file listing.
@@ -52,3 +57,11 @@ type FilePage struct {
 	NextCursor *string
 	PrevCursor *string
 }
+
+// UUIDCreatedAt extracts the creation timestamp embedded in a UUID v7.
+// UUID v7 stores Unix milliseconds in the most-significant 48 bits.
+func UUIDCreatedAt(id uuid.UUID) time.Time {
+	ms := int64(id[0])<<40 | int64(id[1])<<32 | int64(id[2])<<24 |
+		int64(id[3])<<16 | int64(id[4])<<8 | int64(id[5])
+	return time.Unix(ms/1000, (ms%1000)*int64(time.Millisecond)).UTC()
+}

backend/internal/domain/pool.go

@@ -17,7 +17,7 @@ type Pool struct {
 	CreatorName string // denormalized
 	IsPublic    bool
 	FileCount   int
-	CreatedAt   time.Time // extracted from UUID v7
+	CreatedAt   time.Time // extracted from UUID v7 via UUIDCreatedAt
 }
 
 // PoolFile is a File with its ordering position within a pool.
@@ -31,3 +31,11 @@ type PoolFilePage struct {
 	Items      []PoolFile
 	NextCursor *string
 }
+
+// PoolOffsetPage is an offset-based page of pools.
+type PoolOffsetPage struct {
+	Items  []Pool
+	Total  int
+	Offset int
+	Limit  int
+}

backend/internal/domain/tag.go

@@ -20,7 +20,7 @@ type Tag struct {
 	CreatorID     int16
 	CreatorName   string // denormalized
 	IsPublic      bool
-	CreatedAt     time.Time // extracted from UUID v7
+	CreatedAt     time.Time // extracted from UUID v7 via UUIDCreatedAt
 }
 
 // TagRule defines an auto-tagging rule: when WhenTagID is applied,
@@ -31,3 +31,11 @@ type TagRule struct {
 	ThenTagName string // denormalized
 	IsActive    bool
 }
+
+// TagOffsetPage is an offset-based page of tags.
+type TagOffsetPage struct {
+	Items  []Tag
+	Total  int
+	Offset int
+	Limit  int
+}

backend/internal/domain/user.go

@@ -24,7 +24,7 @@ type Session struct {
 	IsCurrent    bool // true when this session matches the caller's token
 }
 
-// OffsetPage is a generic offset-based page of users.
+// UserPage is an offset-based page of users.
 type UserPage struct {
 	Items  []User
 	Total  int