Here is the refactored package structure. I have inferred reasonable implementations for the classes and functions based on standard job queue patterns to ensure the code is functional and demonstrates proper modular design.

### 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 the specific classes and functions from the submodules and exposes them at the package level.

```python
"""
Job Queue Package.

Exports:
    - Job: Dataclass representing a task.
    - JobQueue: Standard FIFO queue for jobs.
    - PriorityQueue: Heap-based queue for prioritized jobs.
    - process_with_retry: Utility for handling job execution with backoff.
"""

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

__all__ = ['Job', 'JobQueue', 'PriorityQueue', 'process_with_retry']
```

### 2. `queue/core.py`
Contains the data model (`Job`) and the basic FIFO queue implementation (`JobQueue`).

```python
from dataclasses import dataclass, field
from datetime import datetime
from typing import Any, Deque, Optional
from collections import deque


@dataclass
class Job:
    """
    Represents a single unit of work.
    
    Attributes:
        id: Unique identifier for the job.
        payload: The data required to perform the task.
        status: Current state (pending, processing, completed, failed).
        retry_count: Number of times this job has been retried.
        created_at: Timestamp when the job was created.
    """
    id: str
    payload: Any
    status: str = "pending"
    retry_count: int = 0
    created_at: datetime = field(default_factory=datetime.now)
    
    def mark_processing(self):
        self.status = "processing"
        self.retry_count += 1

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

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


class JobQueue:
    """
    A standard First-In-First-Out (FIFO) queue for jobs.
    """
    def __init__(self):
        self._queue: Deque[Job] = deque()

    def enqueue(self, job: Job) -> None:
        """Add a job to the end of the queue."""
        self._queue.append(job)

    def dequeue(self) -> Optional[Job]:
        """Remove and return the job at the front of the queue."""
        if self.is_empty():
            return None
        return self._queue.popleft()

    def peek(self) -> Optional[Job]:
        """Return the job at the front without removing it."""
        if self.is_empty():
            return None
        return self._queue[0]

    def is_empty(self) -> bool:
        """Check if the queue has no jobs."""
        return len(self._queue) == 0

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

    def clear(self) -> None:
        """Remove all jobs from the queue."""
        self._queue.clear()
```

### 3. `queue/priority.py`
Implements a priority queue using Python's `heapq` module. It depends on `Job` from `core.py`.

```python
import heapq
from typing import Any, Optional

from .core import Job


class PriorityQueue:
    """
    A priority queue implementation using a min-heap.
    Lower integer values indicate higher priority.
    """
    def __init__(self):
        self._heap: list[tuple[int, int, Job]] = []
        self._counter: int = 0  # To maintain FIFO order for same priority

    def push(self, job: Job, priority: int = 0) -> None:
        """
        Push a job into the queue with a specific priority.
        """
        # Tuple: (priority, insertion_order, job)
        # We use insertion_order to ensure stable sorting if priorities match
        entry = (priority, self._counter, job)
        self._counter += 1
        heapq.heappush(self._heap, entry)

    def pop(self) -> Optional[Job]:
        """
        Remove and return the job with the highest priority (lowest value).
        """
        if not self._heap:
            return None
        _, _, job = heapq.heappop(self._heap)
        return job

    def peek(self) -> Optional[Job]:
        """Return the highest priority job without removing it."""
        if not self._heap:
            return None
        return self._heap[0][2]

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

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

### 4. `queue/retry.py`
Handles the logic for executing a task with exponential backoff on failure.

```python
import time
import math
from typing import Callable, Optional


def process_with_retry(
    func: Callable,
    max_retries: int = 3,
    base_delay: float = 1.0,
    max_delay: float = 60.0,
    *args,
    **kwargs
) -> Optional[any]:
    """
    Execute a function with exponential backoff retry logic.
    
    Args:
        func: The function to execute.
        max_retries: Maximum number of attempts (initial + retries).
        base_delay: Initial delay in seconds.
        max_delay: Maximum cap for the delay.
        *args, **kwargs: Arguments to pass to the function.
        
    Returns:
        The return value of the function if successful.
        
    Raises:
        The last exception raised if all retries are exhausted.
    """
    current_delay = base_delay
    
    for attempt in range(max_retries):
        try:
            return func(*args, **kwargs)
        except Exception as e:
            if attempt == max_retries - 1:
                # Last attempt failed, raise the exception
                raise e
            
            # Calculate backoff: base_delay * (2 ^ attempt)
            next_delay = min(current_delay * 2, max_delay)
            time.sleep(next_delay)
            current_delay = next_delay
            
    return None
```

### Key Design Decisions

1.  **Separation of Concerns**:
    *   `core.py` handles data definitions and basic logic (FIFO).
    *   `priority.py` handles complex data structures (Heaps) specific to ordering.
    *   `retry.py` handles operational logic (network failure handling, sleep timers).
2.  **Dependency Management**:
    *   `priority.py` imports `Job` from `core.py`.
    *   `__init__.py` imports from all submodules.
    *   No circular imports exist.
3.  **Public API**:
    *   Users of the package only need to import from `queue`. They don't need to know about `core` or `priority` files, keeping the namespace clean.
4.  **Extensibility**:
    *   `Job` is a dataclass, making it easy to add fields (e.g., `deadline`, `metadata`) without breaking existing code.
    *   `process_with_retry` is generic, allowing it to wrap any function, not just queue-specific ones.