FIX-#5277: fix internal execute function

[anmyachev]

Signed-off-by: Myachev anatoly.myachev@intel.com

What do these changes do?

• first commit message and PR title follow format outlined here

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• passes flake8 modin/ asv_bench/benchmarks scripts/doc_checker.py
• passes black --check modin/ asv_bench/benchmarks scripts/doc_checker.py
• signed commit with git commit -s
• Resolves BUG: the execute() function that is supposed to trigger execution actually doesn't do so #5277
• tests added and passing
• module layout described at docs/development/architecture.rst is up-to-date

[dchigarev]

Can we add a test to verify that the execute() call "waits" for all of the partitions?

[anmyachev]

Can we add a test to verify that the execute() call "waits" for all of the partitions?

It is much more difficult to write a test if we use wait_partitions function.

UPD: Although no, the same one mock object

[anmyachev]

@dchigarev test is added

[anmyachev]

@dchigarev ready for merge