LeetCode 338: Counting Bits

## [LeetCode 338: Counting Bits](https://leetcode.com/problems/counting-bits/)

**Difficulty:** Easy
**Category:** Bit Manipulation

### Tasks
- [ ] Implement solution in `src/bit_manipulation/counting_bits.py`
- [ ] Verify tests pass: `pytest tests/test_counting_bits.py`
- [ ] Analyze time and space complexity