Fix badge readme and update broken links

[ericpre]

Progress of the PR

• Fix outdated weblink documentation,
• Fix GitHub CI badge and remove drone CI badge,
• [n/a] update docstring (if appropriate),
• [n/a] update user guide (if appropriate),
• add an changelog entry in the upcoming_changes folder (see upcoming_changes/README.rst),
• Check formatting changelog entry in the readthedocs doc build of this PR (link in github checks)
• [n/a] add tests,
• ready for review.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (85cdf6d) 80.25% compared to head (10dbddf) 80.25%.
Report is 2 commits behind head on RELEASE_next_patch.

Additional details and impacted files

@@                 Coverage Diff                 @@
##           RELEASE_next_patch    #3298   +/-   ##
===================================================
  Coverage               80.25%   80.25%           
===================================================
  Files                     147      147           
  Lines                   21859    21859           
  Branches                 5143     5143           
===================================================
  Hits                    17542    17542           
  Misses                   3111     3111           
  Partials                 1206     1206           

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