Here is the refactored code split into the requested package structure.

### 1. `queue/__init__.py`
This file defines the public API. Users of this package will import these symbols directly from the `queue` package.

```python
"""
Queue Package
A modular job queue implementation with priority support and retry logic.
"""

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

# Define the public interface
__all__ = [
    "Job",
    "JobQueue",
    "PriorityQueue",
    "process_with_retry",
]
```

### 2. `queue/core.py`
This module contains the foundational data structures: the `Job` dataclass and the standard FIFO `JobQueue`.

```python
"""
Core Module
Defines the Job data structure and the basic First-In-First-Out (FIFO) queue.
"""

import uuid
from dataclasses import dataclass, field
from typing import Any, Callable, Optional
from collections import deque


@dataclass
class Job:
    """Represents a unit of work to be executed."""
    id: str = field(default_factory=lambda: str(uuid.uuid4()))
    payload: Callable = None
    priority: int = 0
    args: tuple = ()
    kwargs: dict = field(default_factory=dict)


class JobQueue:
    """
    A basic thread-safe FIFO queue implementation.
    """
    def __init__(self):
        self._queue: deque = 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._queue:
            return self._queue.popleft()
        return None

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

### 3. `queue/priority.py`
This module implements the `PriorityQueue`. It relies on `Job` from the core module to determine ordering.

```python
"""
Priority Module
Implements a queue that processes jobs based on priority levels.
"""

import heapq
from typing import Optional

# Import Job from the sibling module
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 = []
        self._counter: int = 0  # Tie-breaker for equal priorities

    def enqueue(self, job: Job) -> None:
        """Add a job to the priority queue."""
        # We use a counter to ensure stability (FIFO) for jobs with same priority
        # and to avoid comparing Job objects directly if priorities match.
        entry = (job.priority, self._counter, job)
        heapq.heappush(self._heap, entry)
        self._counter += 1

    def dequeue(self) -> Optional[Job]:
        """Remove and return the highest priority job."""
        if self._heap:
            priority, count, job = heapq.heappop(self._heap)
            return job
        return None

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

### 4. `queue/retry.py`
This module handles the execution logic with exponential backoff.

```python
"""
Retry Module
Contains logic for executing jobs with automatic retry and backoff.
"""

import time
from typing import Any

# Import Job from the sibling module
from .core import Job


def process_with_retry(
    job: Job, 
    max_retries: int = 3, 
    base_delay: float = 1.0
) -> Any:
    """
    Executes a job's payload. If it fails, it retries with exponential backoff.
    
    Args:
        job: The Job instance containing the payload.
        max_retries: Maximum number of retry attempts.
        base_delay: Initial delay in seconds before the first retry.
        
    Returns:
        The result of the job payload execution.
        
    Raises:
        Exception: If the job fails after max_retries attempts.
    """
    for attempt in range(max_retries):
        try:
            # Execute the payload
            return job.payload(*job.args, **job.kwargs)
        except Exception as e:
            if attempt == max_retries - 1:
                # If this was the last attempt, re-raise the exception
                raise
            
            # Calculate exponential backoff: base_delay * (2 ^ attempt)
            delay = base_delay * (2 ** attempt)
            print(f"Attempt {attempt + 1} failed. Retrying in {delay} seconds...")
            time.sleep(delay)
```