fix: add LearningHeader demo to example app

[awais-ansari]

• Add an authenticated AppContext.Provider rendering LearningHeader with sample
  course org, number, title, and user dropdown enabled
• Add a "Logged in state for Learning header" section heading after the new demo block

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 72.97%. Comparing base (b040bb2) to head (367fe8b).
⚠️ Report is 2 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #668   +/-   ##
=======================================
  Coverage   72.97%   72.97%           
=======================================
  Files          60       60           
  Lines         518      518           
  Branches      108      108           
=======================================
  Hits          378      378           
  Misses        137      137           
  Partials        3        3           

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