fix: Don't re-export client in __init__

[Paillat-dev]

Caution

Feature freeze is active, as described by our Release Schedule.

Summary

Thx @DA-344 @vmphase

Information

• This PR fixes an issue.
• This PR adds something new (e.g. new method or parameters).
• This PR is a breaking change (e.g. methods or parameters removed/renamed).
• This PR is not a code change (e.g. documentation, README, typehinting,
  examples, ...).

Checklist

• I have searched the open pull requests for duplicates.
• If code changes were made then they have been tested.
  • I have updated the documentation to reflect the changes.
• If type: ignore comments were used, a comment is also left explaining why.
• I have updated the changelog to include these changes.
• AI Usage has been disclosed.
  • If AI has been used, I understand fully what the code does

[pycord-app]

Thanks for opening this pull request!
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This pull request can be checked-out with:

git fetch origin pull/3198/head:pr-3198
git checkout pr-3198

This pull request can be installed with:

pip install git+https://github.com/Pycord-Development/pycord@refs/pull/3198/head

[DA-344]

good stuff

[Soheab]

Thank you Mr Plate.