Here is the refactored package structure.

### Implementation Details
1.  **`queue/__init__.py`**: Acts as the public API, re-exporting the main classes and functions for convenient access.
2.  **`queue/core.py`**: Contains the domain model (`Job`) and the high-level manager (`JobQueue`). It imports `PriorityQueue` for storage and `process_with_retry` for execution logic.
3.  **`queue/priority.py`**: Handles the specific data structure logic (heap-based priority queue).
4.  **`queue/retry.py`**: Encapsulates the retry policy and backoff logic.
5.  **Circular Import Handling**: `core.py` defines `Job` *before* importing `process_with_retry` from `retry.py`. This ensures that when `retry.py` imports `Job` from `core`, the class is already available in memory.

### File Structure

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

### Code Content

#### `queue/__init__.py`
```python
"""
Job Queue Package.

Public API exports.
"""
from .core import Job, JobQueue
from .retry import process_with_retry

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

#### `queue/core.py`
```python
"""
Core module containing Job data model and the main JobQueue manager.
"""
import uuid
import time
from datetime import datetime
from typing import Any, Callable, Optional, List
from dataclasses import dataclass, field

# Import priority queue for storage
from .priority import PriorityQueue
# Import retry logic for execution
# Note: We import this after Job definition to avoid circular import issues
# during module initialization.
from .retry import process_with_retry


@dataclass
class Job:
    """Represents a single job to be processed."""
    id: str = field(default_factory=lambda: str(uuid.uuid4()))
    payload: Any = None
    priority: int = 5  # Lower number = higher priority
    status: str = "pending"
    created_at: datetime = field(default_factory=datetime.now)
    retry_count: int = 0
    max_retries: int = 3

    def to_dict(self) -> dict:
        return {
            "id": self.id,
            "payload": self.payload,
            "priority": self.priority,
            "status": self.status,
            "created_at": self.created_at.isoformat(),
            "retry_count": self.retry_count,
            "max_retries": self.max_retries,
        }


class JobQueue:
    """
    Manages the lifecycle of jobs, using a PriorityQueue for ordering.
    """

    def __init__(self):
        self._queue: PriorityQueue = PriorityQueue()
        self._running_jobs: List[Job] = []
        self._handlers: dict[str, Callable] = {}

    def register_handler(self, job_id: str, handler: Callable[[Any], None]):
        """Register a function to handle specific job types."""
        self._handlers[job_id] = handler

    def enqueue(self, payload: Any, priority: int = 5) -> Job:
        """Add a new job to the queue."""
        job = Job(payload=payload, priority=priority)
        self._queue.put(job)
        return job

    def dequeue(self) -> Optional[Job]:
        """Remove and return the highest priority job."""
        return self._queue.get()

    def process(self, job: Job) -> bool:
        """
        Process a specific job using the registered handler and retry logic.
        """
        if job.id not in self._handlers:
            raise ValueError(f"No handler registered for job ID: {job.id}")

        handler = self._handlers[job.id]
        job.status = "running"
        self._running_jobs.append(job)

        try:
            # Execute the job with automatic retry logic
            process_with_retry(handler, job.payload, max_retries=job.max_retries)
            job.status = "completed"
            return True
        except Exception as e:
            job.status = "failed"
            raise e
        finally:
            if job in self._running_jobs:
                self._running_jobs.remove(job)

    def process_next(self) -> bool:
        """
        Dequeue the next job and process it.
        """
        job = self.dequeue()
        if job:
            return self.process(job)
        return False

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

#### `queue/priority.py`
```python
"""
Priority Queue implementation using heapq.
"""
import heapq
from typing import Any, Optional

class PriorityQueue:
    """
    A thread-safe priority queue wrapper around heapq.
    Lower priority values are dequeued first.
    """

    def __init__(self):
        self._heap: list = []
        self._counter: int = 0

    def put(self, item: Any, priority: int = 0):
        """Push an item with a given priority."""
        # heapq in Python is a min-heap, so lower priority value = higher precedence
        # We add a counter to ensure FIFO order for items with equal priority
        entry = (priority, self._counter, item)
        self._counter += 1
        heapq.heappush(self._heap, entry)

    def get(self) -> Optional[Any]:
        """Pop and return the item with the highest priority (lowest value)."""
        if not self._heap:
            return None
        priority, _, item = heapq.heappop(self._heap)
        return item

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

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

#### `queue/retry.py`
```python
"""
Retry logic with exponential backoff.
"""
import time
import random
from typing import Callable, Any
from .core import Job  # Importing Job from core is safe as Job is defined first in core.py

def process_with_retry(
    func: Callable[[Any], None], 
    payload: Any, 
    max_retries: int = 3,
    base_delay: float = 1.0,
    max_delay: float = 60.0
) -> None:
    """
    Execute a function with exponential backoff on failure.
    
    Args:
        func: The function to execute.
        payload: The data to pass to the function.
        max_retries: Maximum number of attempts.
        base_delay: Initial delay in seconds.
        max_delay: Maximum delay cap in seconds.
    """
    attempt = 0
    while attempt <= max_retries:
        try:
            func(payload)
            return  # Success
        except Exception as e:
            attempt += 1
            if attempt > max_retries:
                raise e  # Reraise the final exception
            
            # Calculate backoff with jitter
            delay = min(base_delay * (2 ** (attempt - 1)), max_delay)
            jitter = random.uniform(0, delay * 0.1)
            time.sleep(delay + jitter)
```