FIX-#6967: Remove read_pickle_distributed/to_pickle_distributed functions as deprecated

[anmyachev]

What do these changes do?

• first commit message and PR title follow format outlined here

  NOTE: If you edit the PR title to match this format, you need to add another commit (even if it's empty) or amend your last commit for the CI job that checks the PR title to pick up the new PR title.

• 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 Remove read_pickle_distributed/to_pickle_distributed #6967
• tests added and passing
• module layout described at docs/development/architecture.rst is up-to-date

[YarShev]

Are you aware of the failures in CI?

[anmyachev]

Are you aware of the failures in CI?

Lack of stability in the order of values after the merge function. Restarting helped, but explicit sorting may be required in the future.