SG-41624 Add support for Python 3.13

[julien-lang]

• Add 3.13 to CI tests
• Update badges
• Add 3.13 in README and documentation
• Review deprecated code/information about old Python versions

[Copilot]

Pull request overview

This PR adds documentation build validation and updates CI/CD pipeline configurations. The changes introduce automated Sphinx documentation building during the CI process and modernize the code style validation job with more explicit task configurations.

Key Changes:

• Added automated Sphinx documentation building to the CI pipeline
• Refactored code style validation job to use explicit Bash tasks instead of script shortcuts
• Added flake8 linting to pre-commit hooks

Reviewed changes

Copilot reviewed 4 out of 4 changed files in this pull request and generated 1 comment.

File	Description
azure-pipelines.yml	Added build_documentation template to PR validation jobs
azure-pipelines-templates/code_style_validation.yml	Refactored to use explicit Bash@3 tasks and removed unnecessary properties
azure-pipelines-templates/build_documentation.yml	New template for building Sphinx documentation with Python 3.10 and PySide2
.pre-commit-config.yaml	Added flake8 linting hook for code quality validation

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[Copilot]

Pull request overview

Copilot reviewed 1 out of 1 changed files in this pull request and generated no new comments.

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[Copilot]

Pull request overview

Copilot reviewed 8 out of 8 changed files in this pull request and generated 4 comments.

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[carlos-villavicencio-adsk]

LGTM!

[carlos-villavicencio-adsk]

[codecov]

Codecov Report

❌ Patch coverage is 66.66667% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 77.07%. Comparing base (13be391) to head (9458fc9).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
shotgun_api3/shotgun.py	66.66%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #433      +/-   ##
==========================================
+ Coverage   76.66%   77.07%   +0.40%     
==========================================
  Files          10       10              
  Lines        1890     1880      -10     
==========================================
  Hits         1449     1449              
+ Misses        441      431      -10     

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