Here is the refactored package structure. Since the original implementation wasn't provided, I've reconstructed a production-ready version that matches your described classes/functions while strictly adhering to the requirements.

### `queue/__init__.py`
```python
"""
queue package: Modular job queue implementation with priority and retry support.
"""
from .core import Job, JobQueue
from .priority import PriorityQueue
from .retry import process_with_retry

# Clean public API
__all__ = [
    "Job",
    "JobQueue",
    "PriorityQueue",
    "process_with_retry",
]
```

### `queue/core.py`
```python
"""Core data structures and basic FIFO queue operations."""
from __future__ import annotations

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

@dataclass
class Job:
    """Represents a unit of work to be processed."""
    id: str = field(default_factory=lambda: str(uuid.uuid4()))
    payload: Any = None
    priority: int = 0
    status: str = "pending"
    retry_count: int = 0


class JobQueue:
    """Basic FIFO job queue with standard queue operations."""
    
    def __init__(self) -> None:
        self._queue: deque[Job] = deque()

    def enqueue(self, job: Job) -> None:
        job.status = "queued"
        self._queue.append(job)

    def dequeue(self) -> Optional[Job]:
        if self._queue:
            job = self._queue.popleft()
            job.status = "processing"
            return job
        return None

    def peek(self) -> Optional[Job]:
        return self._queue[0] if self._queue else None

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

    def __len__(self) -> int:
        return len(self._queue)
```

### `queue/priority.py`
```python
"""Priority queue implementation using a min-heap."""
from __future__ import annotations

import heapq
from typing import Optional
from .core import Job

class PriorityQueue:
    """Job queue that orders jobs by priority (lower number = higher priority)."""
    
    def __init__(self) -> None:
        self._heap: list[tuple[int, int, Job]] = []
        self._counter: int = 0  # Tie-breaker for stable sorting

    def enqueue(self, job: Job) -> None:
        job.status = "queued"
        heapq.heappush(self._heap, (job.priority, self._counter, job))
        self._counter += 1

    def dequeue(self) -> Optional[Job]:
        if self._heap:
            _, _, job = heapq.heappop(self._heap)
            job.status = "processing"
            return job
        return None

    def peek(self) -> Optional[Job]:
        if self._heap:
            return self._heap[0][2]
        return None

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

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

### `queue/retry.py`
```python
"""Retry logic with exponential backoff."""
from __future__ import annotations

import time
from typing import Callable, Any, Optional
from .core import Job

def process_with_retry(
    job: Job,
    process_fn: Callable[[Job], Any],
    max_retries: int = 3,
    base_delay: float = 1.0,
    backoff_factor: float = 2.0
) -> Any:
    """
    Execute a job processor with exponential backoff on failure.
    
    Args:
        job: The job to process
        process_fn: Callable that takes a Job and returns the result
        max_retries: Maximum number of retry attempts
        base_delay: Initial delay in seconds before first retry
        backoff_factor: Multiplier for delay between retries
    
    Returns:
        Result from process_fn on success
        
    Raises:
        Exception: The last exception raised if all retries are exhausted
    """
    last_exception: Optional[Exception] = None

    for attempt in range(max_retries + 1):
        try:
            job.retry_count = attempt
            job.status = "processing"
            result = process_fn(job)
            job.status = "completed"
            return result
        except Exception as e:
            last_exception = e
            job.status = "failed"
            if attempt < max_retries:
                delay = base_delay * (backoff_factor ** attempt)
                time.sleep(delay)
            else:
                job.status = "max_retries_exceeded"
                
    raise last_exception  # type: ignore[misc]
```

### Key Design Decisions:
1. **Single Responsibility**: Each module handles one concern: data/FIFO (`core`), ordering (`priority`), fault tolerance (`retry`), and package interface (`__init__`).
2. **Relative Imports**: Uses `.core` syntax to prevent circular dependencies and work correctly when installed as a package.
3. **Consistent Interface**: `JobQueue` and `PriorityQueue` share identical method signatures, allowing them to be swapped via dependency injection.
4. **Type Safety**: Full type hints with `__future__` annotations for forward compatibility and cleaner syntax.
5. **Production Ready**: Includes `__all__` for explicit public API, docstrings, and proper status tracking on the `Job` dataclass.

### Usage Example:
```python
from queue import Job, PriorityQueue, process_with_retry

def my_worker(job: Job):
    if job.payload == "fail":
        raise RuntimeError("Simulated failure")
    return f"Processed {job.id}"

pq = PriorityQueue()
pq.enqueue(Job(payload="success", priority=2))
pq.enqueue(Job(payload="fail", priority=1))

while not pq.is_empty():
    job = pq.dequeue()
    if job:
        try:
            result = process_with_retry(job, my_worker, max_retries=2)
            print(result)
        except Exception as e:
            print(f"Job {job.id} failed after retries: {e}")
```