Sure! Here's a test case generator for the given problem statement:

```python
import random
import string

def generate_string(length):
    return ''.join(random.choices(string.ascii_lowercase, k=length))

def tcgen():
    # Length of the strings (1 ≤ |S| ≤ 2 × 10^5)
    length = random.randint(1, 200000)
    
    # Generate random strings S and T of the same length
    S = generate_string(length)
    T = generate_string(length)
    
    return S, T

# Example usage
S, T = tcgen()
print(S)
print(T)
```

This generator creates random strings `S` and `T` of the same length, ensuring that they fit within the constraints of the problem. You can use this in your competitive programming environment to generate test cases for the given problem.