docs: Rewrite introduction in README and documentation main page

[stotko]

A good introduction in the README and documentation is crucial to get the library's goals, features, and design communicated to users. While our introduction mentions these points, it is a bit wordy and sometimes not easy to immediately grasp. Rewrite it by listing all important aspects briefly in a bullet list. Furthermore, remove redundant parts in the docs version, i.e. the docs main page, and make use of Sphinx design elements.

[codecov]

Codecov Report

Patch and project coverage have no change.

Comparison is base (eacf106) 97.40% compared to head (1eb69f4) 97.40%.

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #401   +/-   ##
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  Coverage   97.40%   97.40%           
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  Files          31       31           
  Lines        2581     2581           
=======================================
  Hits         2514     2514           
  Misses         67       67           

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