Update PyPI publish action

[bouweandela]

Description

• Update the package build and deploy GitHub Action using the latest example from https://packaging.python.org/en/latest/guides/publishing-package-distribution-releases-using-github-actions-ci-cd-workflows/
• Remove outdated setuptools options.

Link to documentation: https://esmvaltool--2939.org.readthedocs.build/projects/ESMValCore/en/2939/how-to/how-to-make-a-release.html#create-and-upload-the-pypi-package

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Before you get started

• ☝ Create an issue to discuss what you are going to do

Checklist

It is the responsibility of the author to make sure the pull request is ready to review. The icons indicate whether the item will be subject to the 🛠 Technical or 🧪 Scientific review.

• 🧪 The new functionality is relevant and scientifically sound
• 🛠 This pull request has a descriptive title and labels
• 🧪 and 🛠 Documentation is available
• 🛠 Changes are backward compatible
• 🛠 The list of authors is up to date
• 🛠 All checks below this pull request were successful

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To help with the number pull requests:

• 🙏 We kindly ask you to review two other open pull requests in this repository

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.59%. Comparing base (82b282f) to head (71c58f2).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #2939   +/-   ##
=======================================
  Coverage   95.59%   95.59%           
=======================================
  Files         266      266           
  Lines       15573    15573           
=======================================
  Hits        14887    14887           
  Misses        686      686           

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[bouweandela]

Tests are failing due to #2940