This refactoring assumes standard Python libraries (like `dataclasses` and `heapq`) are used for the underlying logic.

Here is the content for each file in the target structure:

---

### 📂 `queue/core.py`

This module handles the fundamental data structure (`Job`) and the main queue manager (`JobQueue`).

```python
# queue/core.py
from dataclasses import dataclass, field
from typing import Callable, Any
from .priority import PriorityQueue
import time

@dataclass(order=True)
class Job:
    """
    Represents a single unit of work in the queue.
    The 'priority' field is used for sorting.
    """
    priority: int = field(compare=True)
    id: str = field(compare=False)
    payload: Any = field(compare=False)
    max_retries: int = 3
    attempt_count: int = 0
    
    def __str__(self):
        return f"Job(id={self.id}, priority={self.priority}, attempts={self.attempt_count})"

class JobQueue:
    """
    Manages the collection of jobs using a PriorityQueue.
    This is the primary interface for adding and retrieving jobs.
    """
    def __init__(self):
        # Use the imported PriorityQueue implementation
        self._queue = PriorityQueue()

    def enqueue(self, job: Job):
        """Adds a job to the queue."""
        if not isinstance(job, Job):
            raise TypeError("Input must be a Job object.")
        self._queue.put(job)
        print(f"[{time.strftime('%H:%M:%S')}] Enqueued job: {job.id} (P={job.priority})")

    def dequeue(self) -> Job | None:
        """Removes and returns the highest priority job."""
        return self._queue.get()

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

    def size(self) -> int:
        """Returns the number of jobs currently in the queue."""
        return self._queue.size()

```

### 📂 `queue/priority.py`

This module encapsulates the logic for maintaining priority order, typically using `heapq`.

```python
# queue/priority.py
import heapq
from typing import List, Any

class PriorityQueue:
    """
    Implements a Min-Heap based Priority Queue.
    Items are ordered based on their inherent comparison methods (e.g., Job's priority).
    """
    def __init__(self):
        # The heap stores the elements
        self._heap: List[Any] = []

    def put(self, item: Any):
        """Adds an item to the queue while maintaining heap property."""
        heapq.heappush(self._heap, item)

    def get(self) -> Any:
        """Removes and returns the smallest item (highest priority)."""
        if not self._heap:
            raise IndexError("Cannot get item from empty queue.")
        return heapq.heappop(self._heap)

    def empty(self) -> bool:
        """Returns True if the queue is empty."""
        return not self._heap

    def size(self) -> int:
        """Returns the number of items in the queue."""
        return len(self._heap)
```

### 📂 `queue/retry.py`

This module handles the complex logic of job failure, backoff, and re-queuing.

```python
# queue/retry.py
import time
from typing import Callable, Any
from .core import Job, JobQueue

def exponential_backoff(attempt: int) -> float:
    """Calculates the delay using exponential backoff (2^attempt seconds)."""
    return 2 ** attempt

def process_with_retry(
    job: Job, 
    queue: JobQueue, 
    processing_function: Callable[[Job], bool]
) -> bool:
    """
    Attempts to process a job, implementing retry logic with exponential backoff.

    Args:
        job: The job to process.
        queue: The queue instance to re-enqueue the job if failed.
        processing_function: A function that takes a Job and returns True on success, False on failure.

    Returns:
        True if the job was successfully processed, False if it failed permanently.
    """
    while job.attempt_count < job.max_retries:
        try:
            print(f"\n--- Attempt {job.attempt_count + 1}/{job.max_retries} for Job {job.id} ---")
            
            # 1. Execute the core business logic
            success = processing_function(job)
            
            if success:
                print(f"✅ Job {job.id} successfully completed.")
                return True
            else:
                # The processing function returned False (soft failure)
                raise RuntimeError("Processing function reported failure.")

        except Exception as e:
            job.attempt_count += 1
            print(f"❌ Job {job.id} failed (Attempt {job.attempt_count}): {e}")

            if job.attempt_count >= job.max_retries:
                print(f"🛑 Job {job.id} exceeded max retries. Dropping job.")
                return False
            
            # 2. Calculate backoff time
            wait_time = exponential_backoff(job.attempt_count)
            print(f"⏳ Waiting for {wait_time:.2f} seconds before retry...")
            time.sleep(wait_time)
            
            # 3. Re-enqueue the job
            queue.enqueue(job)
            return False # Indicate that the attempt failed, but it is now scheduled for retry
            
    return False # Should be unreachable if logic is correct, but serves as a final safeguard
```

### 📂 `queue/__init__.py`

This file provides the clean public API for the entire package.

```python
# queue/__init__.py

# Import the core components to expose them directly under the 'queue' namespace
from .core import Job, JobQueue
from .retry import process_with_retry

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

# Example of how to use it:
# from queue import Job, JobQueue, process_with_retry
```

---

### Usage Example (Testing the structure)

To demonstrate how the package works, here is a simple script run outside the `queue` directory:

```python
# main.py
import random
from queue import Job, JobQueue, process_with_retry

# --- Mock Processing Function ---
# This function simulates a job that fails a few times before succeeding.
def mock_processor(job: Job) -> bool:
    """Returns True if the job is 'successful' (e.g., attempt count >= 3), False otherwise."""
    if job.attempt_count < 3 and random.random() < 0.7:
        print(f"   [Processor] Job {job.id} failed this time.")
        return False # Soft failure
    
    print(f"   [Processor] Job {job.id} succeeded!")
    return True # Success

# --- Setup and Run ---
if __name__ == "__main__":
    
    # 1. Initialize the queue
    my_queue = JobQueue()

    # 2. Create jobs
    job1 = Job(id="A1", priority=1, payload={"data": "high_prio"}, max_retries=5)
    job2 = Job(id="B2", priority=5, payload={"data": "low_prio"}, max_retries=3)
    job3 = Job(id="C3", priority=2, payload={"data": "medium_prio"}, max_retries=2)

    # 3. Enqueue jobs
    my_queue.enqueue(job1)
    my_queue.enqueue(job2)
    my_queue.enqueue(job3)

    print("\n--- Starting processing loop ---")

    # 4. Processing loop
    while not my_queue.is_empty():
        # Dequeue the highest priority job
        current_job = my_queue.dequeue()
        
        # Use the retry logic wrapper
        success = process_with_retry(
            job=current_job, 
            queue=my_queue, 
            processing_function=mock_processor
        )

        if success:
            print(f"--- Job {current_job.id} fully done. ---")
        else:
            print(f"--- Job {current_job.id} failed permanently or is waiting for retry. ---")
            
    print("\n--- Queue processing finished. ---")
```