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.

pkg/garmin/types.go

@@ -0,0 +1,27 @@
+package garmin
+
+import "garmin-connect/internal/types"
+
+// GarminTime represents Garmin's timestamp format with custom JSON parsing
+type GarminTime = types.GarminTime
+
+// SessionData represents saved session information
+type SessionData = types.SessionData
+
+// ActivityType represents the type of activity
+type ActivityType = types.ActivityType
+
+// EventType represents the event type of an activity
+type EventType = types.EventType
+
+// Activity represents a Garmin Connect activity
+type Activity = types.Activity
+
+// UserProfile represents a Garmin user profile
+type UserProfile = types.UserProfile
+
+// OAuth1Token represents OAuth1 token response
+type OAuth1Token = types.OAuth1Token
+
+// OAuth2Token represents OAuth2 token response
+type OAuth2Token = types.OAuth2Token