Migrate from Gin to Echo framework and add comprehensive integration tests

Major changes:
- Migrate all handlers from Gin to Echo framework
- Add new apperrors, echohelpers, and validator packages
- Update middleware for Echo compatibility
- Add ArchivedHandler to task categorization chain (archived tasks go to cancelled_tasks column)
- Add 6 new integration tests:
  - RecurringTaskLifecycle: NextDueDate advancement for weekly/monthly tasks
  - MultiUserSharing: Complex sharing with user removal
  - TaskStateTransitions: All state transitions and kanban column changes
  - DateBoundaryEdgeCases: Threshold boundary testing
  - CascadeOperations: Residence deletion cascade effects
  - MultiUserOperations: Shared residence collaboration
- Add single-purpose repository functions for kanban columns (GetOverdueTasks, GetDueSoonTasks, etc.)
- Fix RemoveUser route param mismatch (userId -> user_id)
- Fix determineExpectedColumn helper to correctly prioritize in_progress over overdue

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

internal/apperrors/errors.go

@@ -0,0 +1,97 @@
+package apperrors
+
+import (
+	"fmt"
+	"net/http"
+)
+
+// AppError represents an application error with HTTP status and i18n key
+type AppError struct {
+	Code       int    // HTTP status code
+	Message    string // Default message (fallback if i18n key not found)
+	MessageKey string // i18n key for localization
+	Err        error  // Wrapped error (for internal errors)
+}
+
+func (e *AppError) Error() string {
+	if e.Err != nil {
+		return fmt.Sprintf("%s: %v", e.Message, e.Err)
+	}
+	if e.Message != "" {
+		return e.Message
+	}
+	return e.MessageKey
+}
+
+func (e *AppError) Unwrap() error {
+	return e.Err
+}
+
+// NotFound creates a 404 Not Found error
+func NotFound(messageKey string) *AppError {
+	return &AppError{
+		Code:       http.StatusNotFound,
+		MessageKey: messageKey,
+	}
+}
+
+// Forbidden creates a 403 Forbidden error
+func Forbidden(messageKey string) *AppError {
+	return &AppError{
+		Code:       http.StatusForbidden,
+		MessageKey: messageKey,
+	}
+}
+
+// BadRequest creates a 400 Bad Request error
+func BadRequest(messageKey string) *AppError {
+	return &AppError{
+		Code:       http.StatusBadRequest,
+		MessageKey: messageKey,
+	}
+}
+
+// Unauthorized creates a 401 Unauthorized error
+func Unauthorized(messageKey string) *AppError {
+	return &AppError{
+		Code:       http.StatusUnauthorized,
+		MessageKey: messageKey,
+	}
+}
+
+// Conflict creates a 409 Conflict error
+func Conflict(messageKey string) *AppError {
+	return &AppError{
+		Code:       http.StatusConflict,
+		MessageKey: messageKey,
+	}
+}
+
+// TooManyRequests creates a 429 Too Many Requests error
+func TooManyRequests(messageKey string) *AppError {
+	return &AppError{
+		Code:       http.StatusTooManyRequests,
+		MessageKey: messageKey,
+	}
+}
+
+// Internal creates a 500 Internal Server Error, wrapping the original error
+func Internal(err error) *AppError {
+	return &AppError{
+		Code:       http.StatusInternalServerError,
+		MessageKey: "error.internal",
+		Err:        err,
+	}
+}
+
+// WithMessage adds a default message to the error (used when i18n key not found)
+func (e *AppError) WithMessage(msg string) *AppError {
+	e.Message = msg
+	return e
+}
+
+// Wrap wraps an underlying error
+func (e *AppError) Wrap(err error) *AppError {
+	e.Err = err
+	return e
+}