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/types/garmin.go

@@ -0,0 +1,58 @@
+package types
+
+import "time"
+
+// GarminTime represents Garmin's timestamp format with custom JSON parsing
+type GarminTime struct {
+	time.Time
+}
+
+// SessionData represents saved session information
+type SessionData struct {
+	Domain    string `json:"domain"`
+	Username  string `json:"username"`
+	AuthToken string `json:"auth_token"`
+}
+
+// ActivityType represents the type of activity
+type ActivityType struct {
+	TypeID       int    `json:"typeId"`
+	TypeKey      string `json:"typeKey"`
+	ParentTypeID *int   `json:"parentTypeId,omitempty"`
+}
+
+// EventType represents the event type of an activity
+type EventType struct {
+	TypeID  int    `json:"typeId"`
+	TypeKey string `json:"typeKey"`
+}
+
+// Activity represents a Garmin Connect activity
+type Activity struct {
+	ActivityID      int64        `json:"activityId"`
+	ActivityName    string       `json:"activityName"`
+	Description     string       `json:"description"`
+	StartTimeLocal  string       `json:"startTimeLocal"`
+	StartTimeGMT    string       `json:"startTimeGMT"`
+	ActivityType    ActivityType `json:"activityType"`
+	EventType       EventType    `json:"eventType"`
+	Distance        float64      `json:"distance"`
+	Duration        float64      `json:"duration"`
+	ElapsedDuration float64      `json:"elapsedDuration"`
+	MovingDuration  float64      `json:"movingDuration"`
+	ElevationGain   float64      `json:"elevationGain"`
+	ElevationLoss   float64      `json:"elevationLoss"`
+	AverageSpeed    float64      `json:"averageSpeed"`
+	MaxSpeed        float64      `json:"maxSpeed"`
+	Calories        float64      `json:"calories"`
+	AverageHR       float64      `json:"averageHR"`
+	MaxHR           float64      `json:"maxHR"`
+}
+
+// UserProfile represents a Garmin user profile
+type UserProfile struct {
+	UserName        string     `json:"userName"`
+	DisplayName     string     `json:"displayName"`
+	LevelUpdateDate GarminTime `json:"levelUpdateDate"`
+	// Add other fields as needed from API response
+}