[DOP-13219] Improve documentation

[dolfinus]

Change Summary

• Fixed missing imports in client methods documentation

• Fixed HorizonClientSync example

• Replaced .. code-block:: python + assert ... with doctest-like >>> syntax. It should be more user-friendly (in theory), and it is also more IDE-friendly:
  

• Updated sphinx-copybutton config to avoid copying example outputs

• Fixed changelog validation CI workflow

Compare old docs with new ones

Related issue number

Checklist

• Commit message and PR title is comprehensive
• Keep the change as small as possible
• Unit and integration tests for the changes exist
• Tests pass on CI and coverage does not decrease
• Documentation reflects the changes where applicable
• docs/changelog/next_release/<pull request or issue id>.<change type>.rst file added describing change
  (see CONTRIBUTING.rst for details.)
• My PR is ready to review.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (7ec0ce5) 89.38% compared to head (6415975) 89.38%.

Additional details and impacted files

@@           Coverage Diff            @@
##           develop      #20   +/-   ##
========================================
  Coverage    89.38%   89.38%           
========================================
  Files          103      103           
  Lines         1959     1959           
  Branches       182      182           
========================================
  Hits          1751     1751           
  Misses         162      162           
  Partials        46       46           

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.