cleanup(auth): use full name for google-cloud-gax

[coryan]

Using the gax alias introduces the alias into the examples, which can be confusing.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.02%. Comparing base (d50e7c2) to head (52d809c).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #4597   +/-   ##
=======================================
  Coverage   95.02%   95.02%           
=======================================
  Files         195      195           
  Lines        7458     7458           
=======================================
  Hits         7087     7087           
  Misses        371      371           

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.