refactor: remove redundant test helpers, and use them more

[iFergal]

Separating this from #335 - I am planning on using getOrCreateClient to accept the auth mode (signed headers or ESSR) from the env, so we can add a second integration test run in the matrix.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.53%. Comparing base (78d0a69) to head (d211027).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #336   +/-   ##
=======================================
  Coverage   97.53%   97.53%           
=======================================
  Files           1        1           
  Lines         324      324           
  Branches       24       24           
=======================================
  Hits          316      316           
  Misses          8        8           

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