feat(refactor): Implement 1A.1 Package Structure Refactoring

This commit implements the package structure refactoring as outlined in phase1.md (Task 1A.1).

Key changes include:
- Reorganized packages into `pkg/garmin` for public API and `internal/` for internal implementations.
- Updated all import paths to reflect the new structure.
- Consolidated types and client logic into their respective new packages.
- Updated `cmd/garth/main.go` to use the new public API.
- Fixed various compilation and test issues encountered during the refactoring process.
- Converted `internal/api/client/auth_test.go` to a functional test.

This establishes a solid foundation for future enhancements and improves maintainability.

internal/errors/errors.go

@@ -0,0 +1,84 @@
+package errors
+
+import "fmt"
+
+// GarthError represents the base error type for all custom errors in Garth
+type GarthError struct {
+	Message string
+	Cause   error
+}
+
+func (e *GarthError) Error() string {
+	if e.Cause != nil {
+		return fmt.Sprintf("garth error: %s: %v", e.Message, e.Cause)
+	}
+	return fmt.Sprintf("garth error: %s", e.Message)
+}
+
+// GarthHTTPError represents HTTP-related errors in API calls
+type GarthHTTPError struct {
+	GarthError
+	StatusCode int
+	Response   string
+}
+
+func (e *GarthHTTPError) Error() string {
+	if e.Cause != nil {
+		return fmt.Sprintf("HTTP error (%d): %s: %v", e.StatusCode, e.Response, e.Cause)
+	}
+	return fmt.Sprintf("HTTP error (%d): %s", e.StatusCode, e.Response)
+}
+
+// AuthenticationError represents authentication failures
+type AuthenticationError struct {
+	GarthError
+}
+
+func (e *AuthenticationError) Error() string {
+	if e.Cause != nil {
+		return fmt.Sprintf("authentication error: %s: %v", e.Message, e.Cause)
+	}
+	return fmt.Sprintf("authentication error: %s", e.Message)
+}
+
+// OAuthError represents OAuth token-related errors
+type OAuthError struct {
+	GarthError
+}
+
+func (e *OAuthError) Error() string {
+	if e.Cause != nil {
+		return fmt.Sprintf("OAuth error: %s: %v", e.Message, e.Cause)
+	}
+	return fmt.Sprintf("OAuth error: %s", e.Message)
+}
+
+// APIError represents errors from API calls
+type APIError struct {
+	GarthHTTPError
+}
+
+// IOError represents file I/O errors
+type IOError struct {
+	GarthError
+}
+
+func (e *IOError) Error() string {
+	if e.Cause != nil {
+		return fmt.Sprintf("I/O error: %s: %v", e.Message, e.Cause)
+	}
+	return fmt.Sprintf("I/O error: %s", e.Message)
+}
+
+// ValidationError represents input validation failures
+type ValidationError struct {
+	GarthError
+	Field string
+}
+
+func (e *ValidationError) Error() string {
+	if e.Field != "" {
+		return fmt.Sprintf("validation error for %s: %s", e.Field, e.Message)
+	}
+	return fmt.Sprintf("validation error: %s", e.Message)
+}