Running A Cell In A Background Thread

Better approach to try, running the long running cell in a multiprocessing process, see Python 3 Module of the Week: multiprocessing – Manage processes like threads.
Following your posted example, you’d run:

# Long running cell
import multiprocessing, time

def network_call():
    for i in range(20):
        print(i)
        time.sleep(1)
    
multiprocessing.Process(target=network_call).start()


# Another cell
print("Output from another cell")

This is working in my tests in the classic notebook interface and JupyterLab.
The output from the first cell stays isolated in the first cell as it continues to run and doesn’t pollute elsewhere. Yet, while the first ‘long-running’ cell keeps running, you are able to run the other ‘normal’ cells.