Various documentation enhancements

[bkoelman]

This PR contains various improvements to the documentation website:

• Document public types in the OpenAPI package and show them in API Explorer
• Replace docfx logo with our own
• Enable Google Analytics
• Add redirects for changed APIs (based on 404s from Google Search Console)
• Convert TOCs from Markdown to Yaml format
• Fix caching during local build of the website
• List the example projects in the documentation
• Expand the list of commonly-used types on the API Browser index page
• Add Advanced section in Usage that describes features covered by integration tests
• Consolidate Getting Started to point to the steps in the repo README
• Add GitHub icon in the menu bar

QUALITY CHECKLIST

• Changes implemented in code
• Complies with our contributing guidelines
• N/A: Adapted tests
• Documentation updated

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 90.78%. Comparing base (fe38678) to head (8dae382).
Report is 1 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #1728   +/-   ##
=======================================
  Coverage   90.78%   90.78%           
=======================================
  Files         467      467           
  Lines       14615    14615           
  Branches     2302     2302           
=======================================
  Hits        13268    13268           
  Misses        917      917           
  Partials      430      430           

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