[Python] Python ThreadPoolExecutor: how to submit inside a function submitted

I am using Python's concurrent.futures library with ThreadPoolExecutor and I want to submit inside a function submitted. The following code is a minimal example trying to submit f2 inside submitted f1:

import concurrent.futures


def f2():
print("hello, f2")


def f1():
print("hello, f1")
executor.submit(f2)


with concurrent.futures.ThreadPoolExecutor(16) as executor:
executor.submit(f1)


Output (Python 3.12):

hello, f1


Output is the same even with:

import concurrent.futures


def f2():
print("hello, f2")
return 3


def f1():
print("hello, f1")
print(executor.submit(f2).result())


with concurrent.futures.ThreadPoolExecutor(16) as executor:
executor.submit(f1)


But this code works:

import concurrent.futures


def f2():
print("hello, f2")
return 3


def f1():
print("hello, f1")
return executor.submit(f2).result()


with concurrent.futures.ThreadPoolExecutor(16) as executor:
print(executor.submit(f1).result())


Output:

hello, f1
hello, f2
3


Why f2 is not called in example 1?

Update:

Without the with statement, the output of example 1 is random (i.e. sometimes outputs hello, f2 while sometimes not)


The real use is:

import concurrent.futures


def f3():
print("hello, f3")


def f2():
print("hello, f2")
for i in range(10):
executor.submit(f3)


def f1():
print("hello, f1")
for i in range(10):
executor.submit(f2)


with concurrent.futures.ThreadPoolExecutor(16) as executor:
for i in range(10):
executor.submit(f1)


So I want a simple solution.

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