Here is the refactored package structure. I have created realistic implementations for each component to ensure the functionality matches the requirements while maintaining clean separation of concerns.

### Directory Structure
```text
queue/
├── __init__.py
├── core.py
├── priority.py
└── retry.py
```

### 1. `queue/__init__.py`
This file serves as the public API. It imports high-level components from the submodules and hides internal implementation details.

```python
# queue/__init__.py
"""
Job Queue Package.
Exports: JobQueue, Job, process_with_retry
"""

from .core import Job, JobQueue
from .retry import process_with_retry

__all__ = [
    "Job",
    "JobQueue", 
    "process_with_retry"
]
```

### 2. `queue/core.py`
Contains the data model (`Job`) and the main queue manager (`JobQueue`). It imports `PriorityQueue` from the `priority` module to handle ordering.

```python
# queue/core.py
"""
Core data structures and queue management logic.
"""
from dataclasses import dataclass, field
from typing import Any, Optional
from .priority import PriorityQueue

@dataclass
class Job:
    """Represents a single unit of work."""
    id: str
    payload: Any
    priority: int = 5  # Lower number = higher priority
    status: str = "pending"
    
    def __post_init__(self):
        if self.status not in ["pending", "running", "completed", "failed"]:
            raise ValueError("Invalid job status")

    def mark_running(self):
        self.status = "running"

    def mark_completed(self):
        self.status = "completed"

    def mark_failed(self):
        self.status = "failed"


class JobQueue:
    """
    Manages the lifecycle of Jobs using a Priority Queue.
    """
    def __init__(self):
        self._pq = PriorityQueue()
        self._jobs_by_id = {}

    def enqueue(self, job: Job) -> None:
        """Add a job to the queue."""
        if job.id in self._jobs_by_id:
            raise ValueError(f"Job ID {job.id} already exists")
        
        self._jobs_by_id[job.id] = job
        # PriorityQueue stores tuples: (priority, timestamp, job)
        # timestamp ensures stability if priorities are equal
        import time
        self._pq.push((job.priority, time.time(), job))

    def dequeue(self) -> Optional[Job]:
        """Get the highest priority job. Returns None if empty."""
        if self._pq.is_empty():
            return None
        
        _, _, job = self._pq.pop()
        return job

    def peek(self) -> Optional[Job]:
        """Look at the highest priority job without removing it."""
        if self._pq.is_empty():
            return None
        return self._pq.peek()[2]

    def get_job(self, job_id: str) -> Optional[Job]:
        """Retrieve a specific job by ID."""
        return self._jobs_by_id.get(job_id)

    def size(self) -> int:
        """Return the number of jobs in the queue."""
        return self._pq.size()
```

### 3. `queue/priority.py`
Handles the heap-based sorting logic. It remains generic and does not import `Job` to avoid circular dependencies with `core.py`.

```python
# queue/priority.py
"""
Priority Queue implementation using a min-heap.
"""
import heapq
from typing import Any, List, Optional, Tuple

class PriorityQueue:
    """
    A generic priority queue using heapq.
    Stores tuples of (priority, sequence, item).
    """
    def __init__(self):
        self._heap: List[Tuple[Any, int, Any]] = []
        self._counter = 0

    def push(self, item: Tuple[Any, int, Any]) -> None:
        """Push an item with priority and sequence."""
        priority, sequence, value = item
        heapq.heappush(self._heap, (priority, sequence, value))

    def pop(self) -> Tuple[Any, int, Any]:
        """Pop the item with the highest priority."""
        if not self._heap:
            raise IndexError("Pop from empty queue")
        return heapq.heappop(self._heap)

    def peek(self) -> Tuple[Any, int, Any]:
        """Peek at the highest priority item."""
        if not self._heap:
            raise IndexError("Peek from empty queue")
        return self._heap[0]

    def is_empty(self) -> bool:
        return len(self._heap) == 0

    def size(self) -> int:
        return len(self._heap)
```

### 4. `queue/retry.py`
Contains the business logic for executing jobs with exponential backoff.

```python
# queue/retry.py
"""
Retry logic with exponential backoff.
"""
import time
from typing import Callable, Any
from .core import Job

def process_with_retry(
    job: Job, 
    handler: Callable[[Job], Any],
    max_retries: int = 3,
    base_delay: float = 1.0,
    jitter: float = 0.1
) -> bool:
    """
    Execute a job with exponential backoff retry logic.
    
    Args:
        job: The Job object to process.
        handler: A callable function that accepts the job and returns a result.
        max_retries: Maximum number of retry attempts.
        base_delay: Initial delay in seconds.
        jitter: Random factor to add to delay to prevent thundering herd.
    
    Returns:
        True if the job succeeded, False if it failed after all retries.
    """
    import random
    
    attempts = 0
    
    while attempts <= max_retries:
        try:
            job.mark_running()
            handler(job)
            job.mark_completed()
            return True
        except Exception as e:
            attempts += 1
            job.mark_failed()
            
            if attempts > max_retries:
                break
            
            # Exponential backoff: base_delay * (2 ^ attempts) + jitter
            delay = base_delay * (2 ** attempts) + random.uniform(0, jitter)
            print(f"Job {job.id} failed (attempt {attempts}/{max_retries}). Retrying in {delay:.2f}s...")
            time.sleep(delay)
            
    return False
```

### Key Refactoring Decisions

1.  **Decoupling Data from Logic**: `Job` (data) is separated from `PriorityQueue` (logic). `PriorityQueue` stores generic tuples `(priority, timestamp, item)` so it doesn't need to know about the `Job` object, preventing circular imports.
2.  **Separation of Concerns**:
    *   `core.py` handles the *definition* of a Job and the *container* logic (JobQueue).
    *   `priority.py` handles the *sorting* logic (Heap).
    *   `retry.py` handles the *execution* strategy.
3.  **Public API**: `__init__.py` ensures users only import what they need (`Job`, `JobQueue`, `process_with_retry`), keeping the internal `PriorityQueue` hidden.
4.  **Stability**: The `PriorityQueue` uses a sequence counter (timestamp) alongside priority. This ensures that if two jobs have the same priority, they are processed in the order they were added (FIFO for equal priorities).