fix mypy errors for distributed/dist.py

[puhuk]

What does this PR do?

fix mypy typing errors for distributed/dist.py in #13445

Fixes #<issue_number>

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[carmocca]

Hi! I see this has no fixes yet. Converting to draft

[awaelchli]

@puhuk I think we should close this PR and instead just remove the deprecated module as it's due for removal anyway. The PR #13549 would address this already.

[puhuk]

@awaelchli , Thanks for the feedback and sorry for the delay :)