Real time stdout redirect from a python function call to an async method

So I have a heavy time-consuming function call my_heavy_function and I need to redirect that output to a web interface that is calling it, I have a method to send messages to the web interface, let's called that method async push_message_to_user().

basically, it's something like

import time 

def my_heavy_function():
    time_on = 0 
    for i in range(20):
        time.sleep(1)
        print(f'time spend {time_on}')
        time_on = time_on+1

async def push_message_to_user(message:str):
    # some lib implementation 
    pass

if __name__ == "__main__":
    my_heavy_function() # how push prints to the UI ?
    

maybe there is a way giving my_heavy_function(stdout_obj) and use that "std_object"(StringIO) to do something like stdout_object.push(f'time spend {time_on}'). I can do that, but what I can't change the my_heavy_function() by an async version, to add push_message_to_user() directly instead of the print (it's used by other non-ascyn routines)

what I would want it's something like (pseudocode)

with contextlib.redirect_output(my_prints):
    my_heavy_function()
    while my_prints.readable():
        # realtime push
        await push_message_to_user(my_prints)

Thanks!

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