This refactoring breaks down the responsibilities logically, making the code easier to test, maintain, and scale.

Here is the content for each file in the `queue/` directory.

---

### `queue/priority.py`
*(Handles the specific data structure logic)*

```python
import heapq
from typing import List, Any, Tuple

# We assume Job is defined elsewhere (in core.py) and is comparable.
# For robustness, we'll assume the Job object has a 'priority' attribute.

class PriorityQueue:
    """
    A min-heap implementation of a Priority Queue.
    Items are stored as (priority, insertion_index, item).
    """
    def __init__(self):
        # Heap stores tuples: (priority, index, item)
        self._heap = []
        self._index = 0

    def push(self, item: Any, priority: int):
        """Adds an item with a given priority to the queue."""
        # We use the index as a tie-breaker to ensure stable ordering
        entry = (priority, self._index, item)
        heapq.heappush(self._heap, entry)
        self._index += 1

    def pop(self) -> Any:
        """Removes and returns the item with the highest priority (lowest number)."""
        if not self._heap:
            raise IndexError("pop from empty PriorityQueue")
        # The item is the third element in the tuple
        _, _, item = heapq.heappop(self._heap)
        return item

    def is_empty(self) -> bool:
        """Checks if the queue is empty."""
        return len(self._heap) == 0

    def __len__(self):
        return len(self._heap)
```

### `queue/core.py`
*(Defines the fundamental data structures and the main queue interface)*

```python
from dataclasses import dataclass, field
from typing import Callable
from queue.priority import PriorityQueue

@dataclass(frozen=True)
class Job:
    """Represents a single unit of work."""
    id: str
    task: Callable[[], None]
    priority: int = 0
    max_retries: int = 3
    retry_count: int = 0
    
    def __post_init__(self):
        if not isinstance(self.task, Callable):
            raise TypeError("Job task must be a callable function.")


class JobQueue:
    """
    Manages a collection of Job objects using a PriorityQueue.
    This is the primary interface for the queue system.
    """
    def __init__(self):
        self._queue = PriorityQueue()

    def enqueue(self, job: Job):
        """Adds a job to the queue based on its priority."""
        self._queue.push(job, job.priority)
        print(f"[Queue] Job {job.id} enqueued with priority {job.priority}.")

    def dequeue(self) -> Job:
        """Removes and returns the highest priority job."""
        if self._queue.is_empty():
            raise IndexError("Cannot dequeue from an empty JobQueue.")
        return self._queue.pop()

    def is_empty(self) -> bool:
        """Checks if the queue is empty."""
        return self._queue.is_empty()

    def __len__(self):
        return len(self._queue)
```

### `queue/retry.py`
*(Handles the execution logic and exponential backoff)*

```python
import time
from typing import Callable
from queue.core import Job

def exponential_backoff(attempt: int, base_delay: float = 1.0) -> float:
    """Calculates the delay using exponential backoff: base * 2^attempt."""
    return base_delay * (2 ** attempt)

def process_job_with_retry(job: Job, queue_manager: 'JobQueue') -> bool:
    """
    Executes a job, handling retries with exponential backoff upon failure.

    Args:
        job: The Job object to execute.
        queue_manager: The JobQueue instance used to re-enqueue the job.

    Returns:
        True if the job succeeded, False if it failed permanently.
    """
    
    while job.retry_count <= job.max_retries:
        print(f"\n--- Attempting Job {job.id} (Attempt {job.retry_count + 1}) ---")
        
        try:
            # Execute the actual task
            job.task()
            print(f"[SUCCESS] Job {job.id} completed successfully.")
            return True

        except Exception as e:
            print(f"[FAILURE] Job {job.id} failed: {e}")
            
            if job.retry_count < job.max_retries:
                job.retry_count += 1
                wait_time = exponential_backoff(job.retry_count)
                print(f"[RETRY] Waiting {wait_time:.2f}s before re-enqueueing...")
                time.sleep(wait_time)
                
                # Re-enqueue the job with updated retry count
                queue_manager.enqueue(job)
                return False # Signal that processing needs to continue
            else:
                print(f"[PERMANENT FAILURE] Job {job.id} exceeded max retries ({job.max_retries}). Dropping job.")
                return False # Permanent failure
    
    return False # Should not be reached if logic is correct
```

### `queue/__init__.py`
*(The public API entry point)*

```python
from .core import Job, JobQueue
from .retry import process_job_with_retry

# Export the primary components for easy access
__all__ = [
    "Job",
    "JobQueue",
    "process_job_with_retry"
]
```

---

### Usage Example (How a user would interact with the new package)

If you were to run this code from outside the `queue/` directory:

```python
# main_app.py
from queue import Job, JobQueue, process_job_with_retry
import random

# 1. Define the tasks
def unstable_task():
    # Simulate a failure 2 out of 3 times
    if random.random() < 0.66:
        raise ValueError("Simulated network error.")
    print("Task completed successfully!")

def stable_task():
    print("Stable task running.")

# 2. Initialize the system
queue_manager = JobQueue()

# 3. Create Jobs
job1 = Job(id="J1", task=unstable_task, priority=1, max_retries=3)
job2 = Job(id="J2", task=stable_task, priority=0)
job3 = Job(id="J3", task=unstable_task, priority=2, max_retries=1)


# 4. Enqueue Jobs
queue_manager.enqueue(job1)
queue_manager.enqueue(job2)
queue_manager.enqueue(job3)

print("\n--- Starting Job Processing Loop ---")

# 5. Processing Loop
while not queue_manager.is_empty():
    try:
        # Dequeue the highest priority job
        job_to_run = queue_manager.dequeue()
        
        # Process it, which handles retries and re-queuing
        success = process_job_with_retry(job_to_run, queue_manager)
        
        if not success and job_to_run.retry_count > job_to_run.max_retries:
            print(f"Job {job_to_run.id} was permanently dropped.")

    except IndexError as e:
        print(f"Queue is empty. Stopping.")
        break
```