Update documentation

[hyrodium]

• Add documentation badges to README
• Add @refs to the documentation
• Use julia-repl syntax highlighting
• Remove @contents blocks except for the top page
• Sort sections in the sidebar
• Tables should be left-aligned (cf. my post on discourse)

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 90.18%. Comparing base (0c9b900) to head (efd2f0c).

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #411   +/-   ##
=======================================
  Coverage   90.18%   90.18%           
=======================================
  Files           7        7           
  Lines        1345     1345           
=======================================
  Hits         1213     1213           
  Misses        132      132           

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